# MCQ Questions for Class 12 Maths Chapter 3 Matrices with answers

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Below you will find MCQ Questions of Chapter 3 Matrices Class 12 Maths Free PDF Download that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 3 Matrices with answers

1. (a) A2=A

(b) A3 = A

(c) A2 = O

(d) None of these

► (c) A2 = O

2. For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

(a) det(A) = 9

(b) det(A) = 81

(c) det(A) = 7

(d) det(A) = 4

► (c) det(A) = 7

3. If A any square matrix then which of the following is not symmetric ?

(a) A−At

(b) A+At

(c) AAt

(d) AtA

► (a) A−At

4. For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5

(a) 0

(b) 3

(c) -3

(d) 1

► (b) 3

5. 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

► (d) I ≠ j

6. The number of all possible matrices of order 3×3 with each entry 0 if 1 is

(a) 81

(b) 512

(c) 18

(d) None of these

► (b) 512

7. The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

(a) α not equal to 0

(b) all integral α

(c) all rational α

(d) all real α

► (b) all integral α

8. The inverse of a matrix is defined for

(a) Only square matrices

(b) Diagonal matrices

(c) all matrices

(d) Rectangular matrices

► (a) Only square matrices

9. If A is any square matrix, then

(a) A+At is symmetric

(b) A−At is symmetric

(c) A+At is skew-symmetric

(d) None of these

► (a) A+At is symmetric

10. If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the matrix obtained on multiplying A and B is​

(a) 3×3

(b) 4×1

(c) 3×4

(d) 1×4

► (d) 1×4

11. If A is a matrix of order 3 × 4 , then each row of A has

(a) 12 elements

(b) 3 elements

(c) 4 elements

(d) 7 elements

► (c) 4 elements

12. For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

(a) det(A) = 9

(b) det(A) = 81

(c) det(A) = 7

(d) det(A) = 4

► (c) det(A) = 7

13. If a square matrix A has two identical rows or columns , then det.A is :

(a) 0

(b) -1

(c) 1

(d) None of these

► (a) 0

14. The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have

(a) infinitely many solutions.

(b) only one solution

(c) only two solutions

(d) no solution

► (d) no solution

15. Then the value of x is ____

(a) 6

(b) 3

(c) 2

(d) 0

► (b) 3

16. Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?

(a) Identity matrix

(b) Inverse of A

(c) Square of A

(d) Transpose of A

► (b) Inverse of A

17.  square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for

(a) i is less than j

(b) i = j

(c) iis greater than j

(d) None of these

► (a) i is less than j

18. If A and B are two matrices conformable to multiplication such that their product AB = O(Zero matrix). Then which of the following is true​

(a) A and B are both null matrices

(b) Either of A is or B is a null matrix

(c) Neither of them may be a zero matrix

(d) All of the above options are correct

► (d) All of the above options are correct

19. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique solution if ,

(a) k = 0

(b) − 1 < k < 1

(c) − 2 < k < 2

(d) k ≠ 0

► (d) k ≠ 0

20. What is the element in the 2nd row and 1st column of a 2 x 2 Matrix A = [ aij], such that a = (i + 3) (j – 1)​

(a) 0

(b) 4

(c) -5

(d) 5

► (a) 0

21. If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in

(a) H.P.

(b) G.P.

(c) A.P.

(d) None of these

► (a) H.P.

22. Rank of a non-zero matrix is always

(a) ⩾1

(b) 0

(c) greater than 1

(d) equal to 1

► (a) ⩾1

Hope the given MCQ Questions will help you in cracking exams with good marks. These Matrices MCQ Questions will help you in practising more and more questions in less time.

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