MCQ Questions for Class 12 Maths Chapter 3 Matrices with Answers - Learn Hool

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 3 Matrices with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Matrices Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Matrices Class 12 MCQs Questions with Answers

Question 1.
(left|begin{array}{lll}
3 & 4 & 5 \
0 & 2 & 3 \
0 & 0 & 7
end{array}right|) = A then |A| = ?
(a) 40
(b) 50
(c) 42
(d) 15

Question 2.
The inverse of A = (left|begin{array}{ll}
2 & 3 \
5 & k
end{array}right|) will not be obtained if A has the value
(a) 2
(b) \\(\\frac{3}{2})
(c) \\(\\frac{5}{2})
(d) \\(\\frac{15}{2})

Question 3.
For any unit matrix I
(a) I² = I
(b) |I| = 0
(c) |I| = 2
(d) |I| = 5

Question 4.
A matrix A = [aij]m×n is said to be symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1

Question 5.
If A = (left|begin{array}{lll}
1 & 1 & 1 \
1 & 1 & 1 \
1 & 1 & 1
end{array}right|) then A² is
(a) 27 A
(b) 2 A
(c) 3 A
(d) 1

Question 6.
A matrix A = [aij]m×n is said to be skew symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = -aji
(d) aij = 1

Question 7.
A = [aij]m×n is a square matrix if
(a) m = n
(b) m < n
(c) m > n
(d) None of these

Question 8.
If A and B are square matrices then (AB)’ =
(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’

Question 9.
If A = (left[begin{array}{cc}
cos theta & -sin theta \
sin theta & cos theta
(a) (left[begin{array}{cc}
cos theta & -sin theta \
sin theta & cos theta
end{array}right])
(b) (left[begin{array}{cc}
1 & 0 \
0 & 1
end{array}right])
(c) (left[begin{array}{cc}
cos theta & sin theta \
-sin theta & cos theta
end{array}right])
(d) (left[begin{array}{cc}
-1 & 0 \
0 & -1
end{array}right])

cos theta & sin theta \
-sin theta & cos theta
end{array}right])

Question 10.
If (left[begin{array}{cc}
1-x & 2 \
18 & 6
end{array}right]) = (left[begin{array}{cc}
6 & 2 \
18 & 6
end{array}right]) then x =
(a) ±6
(b) 6
(c) -5
(d) 7

Question 11.
If (left|begin{array}{ll}
x & 8 \
3 & 3
end{array}right|) = 0, the value of x is
(a) 3
(b) 8
(c) 24
(d) 0

Question 12.
If A = (left[begin{array}{cc}
i & 0 \
0 & i
end{array}right]) then A² =
(a) (left[begin{array}{cc}
1 & 0 \
0 & -1
end{array}right])
(b) (left[begin{array}{cc}
-1 & 0 \
0 & -1
end{array}right])
(c) (left[begin{array}{cc}
1 & 0 \
0 & 1
end{array}right])
(d) (left[begin{array}{cc}
-1 & 0 \
0 & 1
end{array}right])

-1 & 0 \
0 & -1
end{array}right])

Question 13.
Let A be a non-singular matrix of the order 2 × 2 then |A-1|=
(a) |A|
(b) \\(\\frac{1}{|A|})
(c) 0
(d) 1

Question 14.
If A = (left[begin{array}{cc}
1 & 2 \
2 & 1
(a) (left[begin{array}{cc}
1 & -2 \
-2 & 1
end{array}right])
(b) (left[begin{array}{cc}
2 & 1 \
1 & 1
end{array}right])
(c) (left[begin{array}{cc}
1 & -2 \
-2 & -1
end{array}right])
(d) (left[begin{array}{cc}
-1 & 2 \
-2 & -1
end{array}right])

1 & -2 \
-2 & 1
end{array}right])

Question 15.
If A = (left[begin{array}{cc}
1 & 1 \
0 & 1
end{array}right]) B = (left[begin{array}{cc}
0 & 1 \
1 & 0
end{array}right]) then AB =
(a) (left[begin{array}{cc}
0 & 0 \
0 & 0
end{array}right])
(b) (left[begin{array}{cc}
1 & 1 \
1 & 0
end{array}right])
(c) (left[begin{array}{cc}
1 & 0 \
0 & 1
end{array}right])
(d) 10

1 & 1 \
1 & 0
end{array}right])

Question 16.
If (left[begin{array}{ccc}
1 & 0 & 0 \
0 & 1 & 0 \
a & b & -1
end{array}right]) then A² =
(a) a unit matrix
(b) A
(c) a null matrix
(d) -A

Question 17.
If A = (left[begin{array}{cc}
α & 0 \
1 & 1
end{array}right]) B = (left[begin{array}{cc}
1 & 0 \
5 & 1
end{array}right]) where A² = B then the value of α is
(a) 1
(b) -1
(c) 4
(d) we cant calculate the value of α

Answer: (d) we cant calculate the value of α

Question 18.
If A = (left[begin{array}{cc}
1 & 2 \
3 & 4
end{array}right]) then
(a) |A| = 0
(b) A-1 exists
(c) A-1 does not exist
(d) None of these

Question 19.
If A = (left[begin{array}{cc}
2x & 5 \
8 & x
end{array}right]) = (left[begin{array}{cc}
6 & -2 \
7 & 3
end{array}right]) then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Question 20.
Let A = (left[begin{array}{cc}
1 & -1 \
2 & 3
end{array}right]) then
(a) A-1 = (left[begin{array}{cc}
frac{3}{5} & frac{1}{5} \
frac{-2}{5} & frac{1}{5}
end{array}right])
(b) |A| = 0
(c) |A| = 5
(d) A² = 1

frac{3}{5} & frac{1}{5} \
frac{-2}{5} & frac{1}{5}
end{array}right])

Question 21.
If A = ( left[begin{array}{ccc}
2 & lambda & -3 \
0 & 2 & 5 \
1 & 1 & 3
end{array}right]) yhen A-1 exists if
(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) none of these

Question 22.
If A = (left[begin{array}{cc}
α & 2 \
2 & α
end{array}right]) and |A³| = 25 then α is
(a) ±3
(b) ±2
(c) ±5
(d) 0

Question 23.
A² – A + I = 0 then the inverse of A
(a) A
(b) A + I
(c) I – A
(d) A – I

Question 24.
If A = (left[begin{array}{cc}
2 & 3 \
1 & -4
end{array}right]) and B = (left[begin{array}{cc}
1 & -2 \
-1 & 3
end{array}right]) then find (AB)-1
(a) \\(\\frac{1}{11}) (left[begin{array}{cc}
14 & 5 \
5 & 1
end{array}right])
(b) \\(\\frac{1}{11}) (left[begin{array}{cc}
14 & -5 \
-5 & 1
end{array}right])
(c) \\(\\frac{1}{11}) (left[begin{array}{cc}
1 & 5 \
5 & 14
end{array}right])
(d) \\(\\frac{1}{11}) (left[begin{array}{cc}
1 & -5 \
-5 & 14
end{array}right])

14 & 5 \
5 & 1
end{array}right])

Question 25.
If A = (left[begin{array}{cc}
3 & 1 \
-1 & 2
end{array}right]) then A² – 5A – 7I is
(a) zero matrix
(b) a diagonal matrix
(c) identity matrix
(d) None of these

Question 26.
If A = (left[begin{array}{cc}
cos x & -sin x \
sin x & cos x
end{array}right]) then A + AT = I if the value of x is
(a) \\(\\frac{π}{6})
(b) \\(\\frac{π}{3})
(c) π
(d) 0

Question 27.
If (left[begin{array}{cc}
x+y & y \
2x & x-y
end{array}right]) (left[begin{array}{c}
2 \
-1
end{array}right]) (left[begin{array}{c}
3 \
2
end{array}right]) then xy equal to
(a) -5
(b) -4
(c) 4
(d) 5

Question 28.
If A = (left[begin{array}{cc}
1 & 2 \
4 & 2
end{array}right]) then |2A| =
(a) 2|A|
(b) 4|A|
(c) 8|A|
(d) None of these

Question 29.
If A = (left[begin{array}{cc}
a & b \
c & d
end{array}right]) then A² is equal to
(a) (left[begin{array}{cc}
a^{2} & b^{2} \
c^{2} & d^{2}
end{array}right])
(b) (left[begin{array}{cc}
b^{2}+bc & ab+bd \
ac+dc & dc+d^{2}
end{array}right])
(c) (left[begin{array}{cc}
a^{3} & b^{3} \
c^{3} & d^{3}
end{array}right])
(d) None of these

b^{2}+bc & ab+bd \
ac+dc & dc+d^{2}
end{array}right])

Question 30.
(left[begin{array}{cc}
cos theta & -sin theta \
-sin theta & cos theta
end{array}right]) is inverse of
(a) (left[begin{array}{cc}
-cos theta & -sin theta \
-sin theta & cos theta
end{array}right])
(b) (left[begin{array}{cc}
cos theta & sin theta \
sin theta & -cos theta
end{array}right])
(c) (left[begin{array}{cc}
cos theta & sin theta \
-sin theta & cos theta
end{array}right])
(d) None of these

cos theta & sin theta \
-sin theta & cos theta
end{array}right])

Question 31.
A = (left[begin{array}{cc}
a & b \
b & a
end{array}right]) and A² = (left[begin{array}{cc}
α & β \
β & α
end{array}right]) then
(a) α = a² + b², β = ab
(b) α = a² + b², β = 2ab
(c) α = a² + b², β = a² – b²
(d) α = 2ab, β = a² + b²

Answer: (b) α = a² + b², β = 2ab

Question 32.
The matrix (left[begin{array}{ccc}
2 & -1 & 4 \
1 & 0 & -5 \
-4 & 5 & 7
end{array}right]) is
(a) a symmetric matix
(b) a skew-sybtmetric matrix
(c) a diagonal matrix
(d) None of these

Question 33.
If a matrix is both symmetric matrix and skew symmetric matrix then
(a) A is a diagonal matrix
(b) A is zero matrix
(c) A is scalar matrix
(d) None of these

Answer: (b) A is zero matrix

Question 34.
If (left[begin{array}{cc}
x+y & 3 \
4 & x-y
end{array}right]) = (left[begin{array}{cc}
1 & 3 \
4 & -3
end{array}right]) then (x, y) is
(a) (-1, 2)
(b) (-1, -2)
(c) (-2, -1)
(d) (1, -2)

Question 35.
The matrix P = (left[begin{array}{ccc}
0 & 0 & 4 \
0 & 4 & 0 \
4 & 0 & 0
end{array}right]) is
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

Question 36.
Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

Question 37.
If (left[begin{array}{cc}
2x+y & 4x \
5x-7 & 4x
end{array}right]) = (left[begin{array}{cc}
7 & 7y-13 \
y & x+6
end{array}right]) then the value of x, y is
(a) 3, 1
(b) 2, 3
(c) 2, 4
(d) 3, 3

Question 38.
If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is
(a) m × 3
(b) 3 × 3
(c) m × n
(d) 3 × n

Question 39.
If A = \\(\\frac{1}{π}) (left[begin{array}{cc}
sin ^{-1}(x pi) & tan^{1}left\\(\\frac{x}{pi}right) \
sin ^{-1}left\\(\\frac{x}{pi}right) & cot ^{-1}(pi x)
end{array}right])
B = \\(\\frac{1}{π}) (left[begin{array}{cc}
cos ^{-1}(x pi) & tan ^{-1}left\\(\\frac{x}{pi}right) \
sin ^{-1}left\\(\\frac{x}{pi}right) & -tan ^{-1}(pi x)
end{array}right])
then A – B equal to
(a) I
(b) O
(c) 1
(d) \\(\\frac{3}{2}) I

Question 40.
If A = (left[begin{array}{cc}
0 & 1 \
1 & 0
end{array}right]) then A² is equal to
(a) (left[begin{array}{cc}
0 & 1 \
1 & 0
end{array}right])
(b) (left[begin{array}{cc}
1 & 0 \
1 & 0
end{array}right])
(c) (left[begin{array}{cc}
0 & 1 \
0 & 1
end{array}right])
(d) (left[begin{array}{cc}
1 & 0 \
0 & 1
end{array}right])

1 & 0 \
0 & 1
end{array}right])

Question 41.
If matrix A = [aij]2×2 where aij = {(_{0 if i = j}^{1 if i ≠ j}) then A² is equal to
(a) I
(b) A
(c) O
(d) None of these

Question 42.
The matrix (left[begin{array}{ccc}
1 & 0 & 0 \
0 & 2 & 0 \
0 & 0 & 0
end{array}right]) is a
(a) identity matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) None of these

Question 43.
The matrix (left[begin{array}{ccc}
0 & -5 & 8 \
5 & 0 & 12 \
-8 & -12 & 0
end{array}right]) is a
(a) diagonal matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) scalar matrix

Question 44.
If A is matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n

Question 45.
If A and B are matrices of same order, then (AB’ – BA’) is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix

Question 46.
If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3 A

Question 47.
For any two matrices A and B, we have
(a) AB = BA
(b) AB ≠ BA
(c) AB = 0
(d) None of these

Question 48.
If A = [aij]2×2 where aij = i + j, then A is equal to
(a) (left[begin{array}{cc}
1 & 2 \
3 & 4
end{array}right])
(b) (left[begin{array}{cc}
2 & 3 \
3 & 4
end{array}right])
(c) (left[begin{array}{cc}
1 & 1 \
2 & 2
end{array}right])
(d) (left[begin{array}{cc}
1 & 2 \
1 & 2
end{array}right])

2 & 3 \
3 & 4
end{array}right])

Question 49.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 18
(b) 512
(c) 81
(d) None of these

Question 50.
The order of the single matrix obtained from
(left[begin{array}{cc}
1 & -1 \
0 & 2 \
2 & 3
end{array}right]) (left{left[begin{array}{ccc}
-1 & 0 & 2 \
2 & 0 & 1
end{array}right]-left[begin{array}{ccc}
0 & 1 & 23 \
1 & 0 & 21
end{array}right]right}) is
(a) 2 × 2
(b) 2 × 3
(c) 3 × 2
(d) 3 × 3

Question 51.
A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) i ≠ j

Question 52.
A square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) None of these

Question 53.
The matrix A = (left[begin{array}{cc}
0 & 1 \
1 & 0
end{array}right]) is a
(a) unit matrix
(b) diagonal matrix
(c) symmetric matrix
(d) skew symmetric matrix

Question 54.
If (left[begin{array}{cc}
x+y & 2x+z\
x-y & 2z+2
end{array}right]) = (left[begin{array}{cc}
4 & 7 \
0 & 10
end{array}right]) then find the value of x, y, z and w respectively
(a) 2, 2, 3, 4
(b) 2, 3, 1, 2
(c) 3, 3, 0, 1
(d) None of these

Answer: (a) 2, 2, 3, 4

Question 55.
If (left[begin{array}{cc}
x-y & 2x+z\
2x-y & 3z+w
end{array}right]) = (left[begin{array}{cc}
-1 & 5 \
0 & 13
end{array}right]) then the value of w is
(a) 1
(b) 2
(c) 3
(d) 4

Question 56.
Find x, y, z and w respectively such that
(left[begin{array}{cc}
x-y & 2x+z\
2x-y & 2x+w
end{array}right]) = (left[begin{array}{cc}
5 & 3 \
12 & 15
end{array}right])
(a) 7, 2, 1, 1
(b) 7, 5, 3, 8
(c) 1, 2, 5, 6
(d) 6, 3, 2, 1

Answer: (a) 7, 2, 1, 1

Question 57.
If (left[begin{array}{cc}
a+b & 2\
5 & ab
end{array}right]) = (left[begin{array}{cc}
6 & 2 \
5 & 8
end{array}right]) then find the value of a and b respectively
(a) 2, 4
(b) 4, 2
(c) Both (a) and (b)
(d) None of these

Answer: (c) Both (a) and (b)

Question 58.
For what values of x and y are the following matrices equal
A = (left[begin{array}{cc}
2x+1 & 3y\
0 & y^{2}-5y
end{array}right]) B = (left[begin{array}{cc}
x+3 & y^{2}+2 \
0 & -6
end{array}right])
(a) 2, 3
(b) 3, 4
(c) 2, 2
(d) 3, 3

Question 59.
If A = (left[begin{array}{cc}
α & 0\
1 & 1
end{array}right]) and B = (left[begin{array}{cc}
1 & 0 \
5 & 1
end{array}right]) then find value of α for which A² = B is
(a) 1
(b) -1
(c) 4
(d) None of these

Question 60.
If P = (left[begin{array}{ccc}
i & 0 & -i \
0 & -i & i \
-i & i & 0
end{array}right]) and Q = (left[begin{array}{cc}
-i & i \
0 & 0 \
i & -i
end{array}right]) then PQ is equal to
(a) (left[begin{array}{cc}
-2 & 2 \
1 & -1 \
1 & -1
end{array}right])
(b) (left[begin{array}{cc}
2 & -2 \
-1 & 1 \
-1 & 1
end{array}right])
(c) (left[begin{array}{cc}
2 & -2\
-1 & 1
end{array}right])
(d) (left[begin{array}{ccc}
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
end{array}right])

2 & -2 \
-1 & 1 \
-1 & 1
end{array}right])

Question 61.
(left[begin{array}{c}
1 & x & 1
end{array}right]) (left[begin{array}{ccc}
1 & 3 & 2 \
2 & 5 & 1 \
15 & 3 & 2
end{array}right]) (left[begin{array}{c}
1 \
2 \
x
end{array}right])
(a) -7
(b) -11
(c) -2
(d) 14

Question 62.
If A = (left[begin{array}{cc}
1 & -1\
2 & -1
end{array}right]) B = (left[begin{array}{cc}
x & 1\
y & -1
end{array}right]) and (A + B)² = A² + B², then x + y is
(a) 2
(b) 3
(c) 4
(d) 5

Question 63.
If AB = A and BA = B, then
(a) B = 1
(b)A = I
(c) A² = A
(d) B² = I

Question 64.
If A = (left[begin{array}{ccc}
1 & 0 & 0 \
0 & 1 & 0 \
a & b & -1
end{array}right]) then (A – I) (A + I) = 0 for
(a) a = b = 0 only
(b) a = 0 only
(c) b = 0 only
(d) any a and b

Answer: (d) any a and b

Question 65.
If A = (left[begin{array}{cc}
1 & 1\
0 & 2
end{array}right]) then A8 – 28 (A – I)
(a) I – A
(b) 2I – A
(c) I + A
(d) A – 2I

Question 66.
If A = (left[begin{array}{ccc}
2 & 2 & 1 \
1 & 3 & 1 \
1 & 2 & 2
end{array}right]) then A³ – 7A² + 10A =
(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I

Question 67.
If A is a m × n matrix such that AB and BA are both defined, then B is an
(a) m × n matrix
(b) n × m matrix
(c) n × n matrix
(d) m × m matrix

Answer: (b) n × m matrix

Question 68.
If A = (left[begin{array}{cc}
1 & 2\
3 & 4
end{array}right]) then A2 – 5A is equal to
(a) 2I
(b) 3I
(c) -2I
(d) null matrix

Question 69.
If A = (left[begin{array}{cc}
-2 & 4\
-1 & 2
end{array}right]) then A2 is
(a) null matrix
(b) unit matrix
(c) (left[begin{array}{cc}
0 & 0\
0 & 0
end{array}right])
(d) (left[begin{array}{cc}
0 & 0\
0 & 1
end{array}right])

Question 70.
If A and B are 2 × 2 matrices, then which of the following is true?
(a) (A + B)² = A² + B² + 2AB
(b) (A – B)² = A² + B² – 2AB
(c) (A – B)(A + B) = A² + AB – BA – B²
(d) (A + B) (A – B) = A² – B²