11. If A =

1 1

1 1

sin ( ) tan1

sin cot ( )

xx

x x

, B =

1 1

1 1

cos ( ) tan1

sin tan ( )

xx

x x

, then

A B is equal to

(A) I (B) O (C) 2I (D) 1 I2

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

(A) m 3 (B) 3 3 (C) m n (D) 3 n

13. If A =0 11 0

, then A2 is equal to

(A)0 11 0

(B)1 01 0

(C)0 10 1

(D)1 00 1

14. If matrix A = [aij]2 2, where aij = 1 if i j

= 0 if i = j

then A2 is equal to

(A) I (B) A (C) 0 (D) None of these

15. The matrix

1 0 00 2 00 0 4

is a

(A) identity matrix (B) symmetric matrix

(C) skew symmetric matrix (D) none of these

MATRICES 61

16. The matrix

0 5 85 0 128 12 0

is a

(A) diagonal matrix (B) symmetric matrix

(C) skew symmetric matrix (D) scalar matrix

17. If A is matrix of order m n and B is a matrix such that AB and BA are bothdefined, then order of matrix B is

(A) m m (B) n n

(C) n m (D) m n

18. If A and B are matrices of same order, then (ABBA) is a

(A) skew symmetric matrix (B) null matrix

(C) symmetric matrix (D) unit matrix

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

(A) A (B) I A (C) I + A (D) 3A

20. For any two matrices A and B, we have

(A) AB = BA (B) AB BA

(C) AB = O (D) None of the above

21. On using elementary column operations C2 C2 2C1 in the following matrixequation

1 32 4

= 1 10 1

3 12 4

, we have :

(A)1 50 4

= 1 12 2

3 52 0

(B)1 50 4

= 1 10 1

3 50 2

(C)1 52 0

= 1 30 1

3 12 4

(D)1 52 0

= 1 10 1

3 52 0

22. On using elementary row operation R1 R1 3R2 in the following matrix equation:

4 23 3

= 1 20 3

2 01 1

, we have :

(A)5 7

3 3

= 1 70 3

2 01 1

(B)5 7

3 3

= 1 20 3

1 31 1

(C)5 7

3 3

= 1 21 7

2 01 1

(D)4 25 7

= 1 23 3

2 01 1