Please refer to MCQ Questions Chapter 3 Matrices Class 12 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 12 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 12 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 3 Matrices in Class 12 Mathematics provided below to get more marks in exams.

**Chapter 3 Matrices MCQ Questions**

**Question. If A= [aij] mxn and B= [bij]pxq and AB= BA then **

(a) n=p

(b) n=p, m=n

(c) m=n=p=q

(d) m=q

**Answer**

C

**Question: 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

**Answer**

A

**Question: If a, b and c are all different from zero such that 1/a +1/b +1/c=0, then the matrix**(a) symmetric

(b) non-singular

(c) can be written as sum of a symmetric and a skew-symmetric matrix

(d) All of the above

**Answer**

D

**Question: For what value of x, the matrix**

**is singular**

(a) x = 1, 2

(b) x = 0, 2

(c) x = 0, 1

(d) x = 0 ,3

**Answer**

D

**Question**:

(a) 4

(b) 3

(c) -4

(d) -3

**Answer**

C

**Question: For any 2x 2 matrix A, if A (a d j A) =**

** then |A | is equal to**(a) 0

(b) 10

(c) 20

(d) 100

**Answer**

B

**Question: The matrix A =**

**is**

(a) unitary

(b) orthogonal

(c) nilpotent

(d) involutory

**Answer**

C

**Question:**

**Answer**

A

**Question: If A is a singular matrix, then A adj (A )**(a) is a scalar matrix

(b) is a zero matrix

(c) is an identity matrix

(d) is an orthogonal matrix

**Answer**

B

**Question: **

(a) A is singular

(b) | | A ¹ 0

(c) A is symmetric

(d) None of these

**Answer**

A

**Question:**

(a) A

(b)| A|

(c) |A | I

d) None of these

**Answer**

C

**Question: Matrix A =**

**is invertible for**

(a) k = 1

(b) k = – 1

(c) k = ± 1

(d) None of these

**Answer**

C

**Question:**

(a) A

(b) |A|

(c) |A|I

(d) None of these

**Answer**

A

**Question: If A is a skew-symmetric matrix of odd order, then A| is equal to**(a) 0

(b) n

(c) n

^{2}

(d) None of these

**Answer**

A

**Question:**

(a) 12^{4}

(b) 13^{4}

(c) 14^{4}

(d) None of these

**Answer**

C

**Question: **

**Answer**

C

**Question:**

(a) 5

(b) 25

(c) –1

(d) 1

**Answer**

D

**Question:**

(a) 0

(b) – 1

(c) 1

(d) |A|

**Answer**

D

**Question: If A ^{2}– A+I = 0, then the inverse of A is**

a) A- I

(b) I- A

(c) A + 1

(d) A

**Answer**

B

**Question:**

(a) A

(b) A’

(c) 3A

(d) 3A

**Answer**

D

**Question:**

(a) – 1 6

(b) 1/ 3

(c) – 1/ 3

(d) 1/ 6

**Answer**

A

**Question. If A is of order 2x ^{3} and B is of order 3x^{2}, then the order of AB is : **

(a) 3x

^{3}

(b) 2x

^{2}

(c) 3x

^{2}

(d) 2x

^{3}

**Answer**

B

**Question. **

(a) 5A

(b) 10A

(c) 16 A

(d) 32 A

**Answer**

C

**Question. **

**Answer**

B

**Question. **

**Answer**

A

**Question. **

(a) (3,7)

(b) (9,14)

(c) (5,14)

(d) (3,14)

**Answer**

B

**Question. **

(a) I

(b) 2I

(c) 3I

(d) 4A

**Answer**

B

**Question. If A is a square matrix , then AA ^{T} + A^{T}A is : **

(a) Unit matrix

(b) null matrix

(c) symmetric matrix

(d) skew-symmetric matrix

**Answer**

C

**Question. If a _{ij}= i + j then A = [𝑎_{𝑖𝑗}]3×4 is : **

**Answer**

B

**Question. **

**Answer**

C

**Question. **

(a) (2,4), (4,2)

(b) (3,3),(3,4)

(c) (2,2),(1,1)

(d) none of above

**Answer**

A

**Question. **

(a) 1

(b) 2

(c) 1/2

(d) -2

**Answer**

C

**Question. **

**Answer**

C

**Question. **

(a) -5

(b) -1/5

(c) 1/25

(d) 25

**Answer**

B

**Question. **

(a) a = 2, b = -3

(b) a = -2, b = -3

(c) a = 1, b = 4

(d) none of above

**Answer**

C

**Question. **

(a) 0

(b) I2

(c) -I2

(d) none of these

**Answer**

A

**Question. **

**Answer**

C

**Question. **

** **(d) none of above

**Answer**

C

**Question.**

(a) 1/3

(b) 5

(c) 3

(d) 1

**Answer**

A

**Question. **

**Answer**

B

**Question.**

(a) x = 3,y =1

(b) x = 2,y = 3

(c) x = 2,y = 4

(d) x = 3,y = 3

**Answer**

B

**Question. Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is**(a) 9

**(b) 27**

(c) 81

(d) 512

**Answer**

A

**Question.** If A and B are two matrices of the order 3 x m and 3 x n, respectively and m = n, then order of matrix (5A – 2B) is

(a)m x 3

(b) 3 x 3

(c)m x n

(d) 3 x n

**Answer**

D

**Question.**

(a) I

(b) 0

(c) 2I

(d) (1/2)I

**Answer**

D

**Question.**

(a) square matrix

(b) diagonal matrix

(c) unit matrix

(d) None of these

**Answer**

A

**Question.**

(a) diagonal matrix

(b) symmetric matrix

(c) skew-symmetric matrix

(d) scalar matrix

**Answer**

C

**Question.****On using elementary row operation R _{1} → R_{1} – 3R_{2} in the following**

**Answer**

A

**Question.** If A is a square matrix such that A^{2} = I, then (A – I)^{3} + (A + I)^{3} – 7A is equal to

(a) A

(b) I – A

(c) I + A

(d) 3A

**Answer**

A

**Question.** If A is matrix of order m x n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is

(a) m x m

(b) n x n

(c) n x m

(d) m x n

**Answer**

D

**Question.** If matrix A =[ a_{ij} ]_{2×2}, where a_{ij} = 1, if i ≠ j = 0 and if i = j, then A^{2} is equal to

(a) I

(b) A

(c) 0

(d) None of these

**Answer**

A

**Question.**

(a) identity matrix

(b) symmetric matrix

(c) skew-symmetric matrix

(d) None of these

**Answer**

B

**Question.** 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

**Answer**

A

**Question.****On using elementary column operations C _{2} → C_{2} – 2C_{1} in the**

**Answer**

D

**Question.****For any two matrices A and B, we have**(a) AB = BA

(b) AB ≠ BA

(c) AB = O

(d) None of these

**Answer**

D

**True/False**

**Question.** Two matrices are equal, if they have same number of rows and same number of columns.

**Answer**

False

**Question.** Matrices of different order cannot be subtracted.

**Answer**

True

**Question.** A matrix denotes a number.

**Answer**

False

**Question.** Matrices of any order can be added.

**Answer**

False

**Question.** If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.

**Answer**

False

**Question.** Matrix multiplication is commutative.

**Answer**

False

**Question.** A square matrix where every element is unity is called an identity matrix.

**Answer**

False

**Question.** Matrix addition is associative as well as commutative.

**Answer**

True

**Question.** If A and B are two matrices of the same order, then A – B = B – A.

**Answer**

False

**Question.** If A and B are two square matrices of the same order, then A + B = B + A.

**Answer**

True

**Question.** If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

**Answer**

False

**Question.** If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

**Answer**

True

**Question.** If A and B are any two matrices of the same order, then (AB)’ = A’B’.

**Answer**

False

**Question.** If A is skew-symmetric matrix, then A^{2} is a symmetric matrix.

**Answer**

True

**Question.** Transpose of a column matrix is a column matrix.

**Answer**

False

**Question.** If A and B are two square matrices of the same order, then AB = BA.

**Answer**

False

**Question.** If (AB)’ = B’ A’, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

**Answer**

True

**Question.** (AB)^{-1} = A-1 · B^{-1}, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

**Answer**

True

**Question.** AA’ is always a symmetric matrix for any matrix A.

**Answer**

True

**Question.**

**Answer**

False

We hope you liked the above provided **MCQ Questions Chapter 3 Matrices Class 12 Mathematics** with solutions. If you have any questions please ask us in the comments box below.