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## Matrices Class 12 MCQs Questions with Answers

Students are advised to solve the Matrices Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Matrices Class 12 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Matrices Class 12 with answers provided with detailed solutions by looking below.

Question 1.

If A = [a_{ij}]_{m × n} is a square matrix, if:

(a) m < n

(b) m > n

(c) m = n

(d) None of these.

## Answer

Answer: (c) m = n

Question 2.

Which of the given values of x and y make the following pair of matrices equal:

\(\left[\begin{array}{cc}

3 x+7 & 5 \\

y+1 & 2-3 x

\end{array}\right]\) \(\left[\begin{array}{lc}

0 & y-2 \\

8 & 4

\end{array}\right]\)

(a) x = –\(\frac { 1 }{3}\), y = 7

(b) Not possible to find

(c) y = 7, x = –\(\frac { 2 }{3}\)

(d) x = –\(\frac { 1 }{3}\), y = –\(\frac { 2 }{3}\)

## Answer

Answer: (b) Not possible to find

Question 3.

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is

(a) 27

(b) 18

(c) 81

(d) 512.

## Answer

Answer: (d) 512.

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × 1, 2 × p, n × 3 and p × k respectively. Now answer the following (4-5):

Question 4.

The restrictions on n, k and p so that PY + WY will be defined are

(a) k = 3, p = n

(b) k is arbitrary, p = 2

(c) p is arbitrary

(d) k = 2,p = 3.

## Answer

Answer: (a) k = 3, p = n

Question 5.

If n =p, then the order of the matrix 7X – 5Z is:

(a) p × 2

(b) 2 × n

(c) n × 3

(d) p × n.

## Answer

Answer: (b) 2 × n

Question 6.

If A, B are symmetric matrices of same order, then AB – BA is a

(a) Skew-symmetric matrix

(b) Symmetric matrix

(c) Zero matrix

(d) Identity matrix.

## Answer

Answer: (a) Skew-symmetric matrix

Question 7.

If A = \(\left[\begin{array}{l}

\cos \alpha-\sin \alpha \\

\sin \alpha \cos \alpha

\end{array}\right]\) then A + A’ = I, the value of α is

(a) \(\frac { π }{6}\)

(b) \(\frac { π }{3}\)

(c) π

(d) \(\frac { 3π }{2}\)

## Answer

Answer: (a) \(\frac { π }{6}\)

Question 8.

Matrices A and B will be inverse of each other only if:

(a) AB = BA

(b) AB – BA = O

(c) AB = O, BA = I

(d) AB = BA = I.

## Answer

Answer: (d) AB = BA = I.

Question 9.

If A = \(\left[\begin{array}{lr}

\alpha & \beta \\

\gamma & -\alpha

\end{array}\right]\) is such that A² = I, then

(a) 1 + α² + ßγ = 0

(b) 1 – α² + ßγ = 0

(c) 1 – α² – ßγ = 0

(d) 1 + α² – ßγ = 0

## Answer

Answer: (c) 1 – α² – ßγ = 0

Question 10.

If a matrix is both symmetric and skew- symmetric matrix, then:

(a) A is a diagonal matrix

(b) A is a zero matrix

(c) A is a square matrix

(d) None of these.

## Answer

Answer: (b) A is a zero matrix

Question 11.

If A is a square matrix such that A² = A, then (I + A)³ – 7A is equal to :

(a) A

(b) I – A

(c) I

(d) 3A.

## Answer

Answer: (c) I

Question 12.

The matrix A = \(\left[\begin{array}{lll}

0 & 0 & 5 \\

0 & 5 & 0 \\

5 & 0 & 0

\end{array}\right]\) is a

(a) scalar matrix

(b) diagonal matrix

(c) unit matrix

(d) square matrix.

## Answer

Answer: (d) square matrix.

Question 13.

If matrix A = [a_{ij}]_{2×2}

where a_{ij} = 1 if i ≠ j = 0 if i = j,

(a) I

(b) A

(c) O

(d) None of these

## Answer

Answer: (a) I

Question 14.

then A – B is equal to

(a) I

(b) O

(c) 2I

## Answer

Answer: (c) 2I

Question 15.

If A is a 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.

## Answer

Answer: (d) m × n.

Question 16.

For any two matrices A and B, we have :

(a) AB = BA

(b) AB ≠ BA

(c) AB = 0

(d) None of these.

## Answer

Answer: (d) None of these.

Question 17.

The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:

(a) less than 4

(b) 5

(c) 6

(d) at least 7.

## Answer

Answer: (d) at least 7.

Hint:

First row with exactly one zero total number of cases = 6.

First row with 2 zeroes, we get more cases.

∴ Total no. of non-singular matrices = 7.

Question 18.

If A is an 3 × 3 non-singular matrix such that AA’ = A’A and B = A^{-1} A’, then BB’ equals

(a) I

(b) B^{-1}

(c) (B^{-1})’

(d) I + B.

## Answer

Answer: (a) I

B = A^{-1}A’

⇒ AB = A’

ABB’ = A’B’

⇒ ABB’ = (BA)’ = (A^{-1} A’A)’

= (A^{-1} AA’)’ = (A’)’ = A

BB’ = I.

Fill in the Blanks

Question 1.

If \(\left[\begin{array}{ll}

1 & 2 \\

2 & 1

\end{array}\right]\) \(\left[\begin{array}{l}

x \\

y

\end{array}\right]\) = \(\left[\begin{array}{l}

5 \\

4

\end{array}\right]\) then value of y is ………………..

## Answer

Answer: 2.

Question 2.

If A is an m × n matrix such that AB and BA are defind, then B is of order …………….

## Answer

Answer: n × m.

Question 3.

A diagonal matrices is said to be ……………… if its diagonal elements are equal (other than unity).

## Answer

Answer: scalar.

Question 4.

For a 2 × 2 matrix, A = [a_{ij}], whose elements are given by a_{ij} = \(\frac { i }{j}\), then a_{12} = ………………..

## Answer

Answer: \(\frac {1}{2}\)

Question 5.

If \(\left[\begin{array}{cc}

a-b & 2 a+c \\

2 a-b & 3 c+d

\end{array}\right]\) = \(\left[\begin{array}{cc}

-1 & 5 \\

0 & 13

\end{array}\right]\)

## Answer

Answer: 1

Question 6.

If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the ……………….

## Answer

Answer: inverse of A.

Question 7.

If A is of order m × n and B is also of order m × n, then (A + B) is a matrix of order ………………..

## Answer

Answer: m × n.

Question 8.

If [5 x 1] \(\left[\begin{array}{l}

4 \\

2 \\

7

\end{array}\right]\) = 35 then x = ………………

## Answer

Answer: 4

Question 9.

For any matrix A, A – A’ is …………….. matrix.

## Answer

Answer: Skew-symmetric.

Question 10.

If A = \(\left[\begin{array}{cc}

2 & -2 \\

-2 & 2

\end{array}\right]\) and A² = λA, then λ = ………………..

## Answer

Answer: 4

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