These MCQ On Matrices Class 12 PDFs are most important for your upcoming examinations including JEE Main & JEE Advanced. These MCQ On Matrices Class 12 will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## MCQ On Matrices Class 12 PDF Download

1. If A and B are matrices of the same order, then (AB’ – BA’) is a

(A) skew-symmetric matrix

(B) null matrix

(C) symmetric matrix

(D) unit matrix

**Answer:** skew symmetric matrix

2. A square matrix A = [a_{ij}]_{n×n}is called a diagonal matrix if a_{ij} = 0 for

(A) i = j

(B) i < j

(C) i > j

(D) i ≠ j

**Answer:** i ≠ j

3. 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

**Answer:** (A – B)(A + B) = A² + AB – BA – B²

4. A = [a_{ij}]_{m×n}is a square matrix if

(A) m = n

(B) m < n

(C) m > n

(D) None of these

**Answer:** m = n

5. If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order

(A) 2 x 3

(B) 2 x 2

(C) 3 x 2

(D) 3 x 3

**Answer:** 2 x 2

6. If a matrix has 24 elements then the number of possible orders it can have, is

(A) 6

(B) 8

(C) 12

(D) 16

**Answer:** 8

7. If A and B are two matrices such that both AB and BA are defined, then

(A) A and B can be any two matrices.

(B) A and B are not square matrices not necessarily of the same order.

(C) A and B are square matrices of the same order.

(D) a number of columns of A = number of rows of B.

**Answer:** A and B are not square matrices not necessarily of the same order.

8. If A is an orthogonal matrix then A^{T}is a/an

(A) identity matrix

(B) null matrix

(C) orthogonal matrix

(D) scalar matrix

**Answer:** orthogonal matrix

9. If A = [3 4 7 -1] [1 6 7 2] [9 8 6 4] then the order of the matrix is

(A) 4 * 3

(B) 3 * 4

(C) 3 * 3

(D) 4 * 4

**Answer:** 3 * 4

10. If 2[3 4] + [1 y] = [7 0] [5 x] [0 1] [10 5] then the value of x – y is

(A) 8

(B) 10

(C) -8

(D) -10

**Answer:** 10

11. If A = [ 2 -3 -1 4] then the matrix B such that 2A + 3B = 0 is

(A) [4/3 2 2/3 -8/3]

(B) [-4/3 2 2/3 8/3]

(C) [-4/3 2 2/3 -8/3]

(D) [-4/3 2 -2/3 -8/3]

**Answer:** [-4/3 2 2/3 -8/3]

12. If A is a skew-symmetric matrix of order 3, then the value of determinant A is

(A) 0

(B) 1

(C) -1

(D) None of these

**Answer:** 0

13. If A = then find value of α for which A² = B is

(A) 1

(B) -1

(C) 4

(D) None of these

**Answer:** None of these

14. If A = then A^{8}– 2^{8} (A – I)

(A) I – A

(B) A

(C) I + A

(D) A – 2I

**Answer:** 2I – A

15. If A = then A^{2}– 5A is equal to

(A) 2I

(B) 3I

(C) -2I

(D) null matrix

**Answer:** 2I

16. If A = B = then A – B equal to

(A) I

(B) O

(C) 1

(D) 3/2 |

**Answer:** 3/2 |

17. If 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:** 2, 2, 3, 4

18. If A = then the value of x is

(A) 3

(B) ±3

(C) ±6

(D) 6

**Answer:** 3

19. If A is a square matrix, then A is symmetric iff

(A) A^{2} = A

(B) A^{2} = I

(C) A^{t} = A

(D) A^{t} = – A

**Answer:** A^{t} = A

20. If A is any square matrix, then

(A) A + A^{t} is symmetric

(B) A – A^{t} is symmetric

(C) AA^{t} is scew symmetric

(D) none of these

**Answer:** A + A^{t} is symmetric