1. A matrix A for which AP = 0 where P is a positive integer is called
(a) skew symmetric
(b) unit matrix
(c) symmetric
(d) nilpotent
2. If A = 0 4
0 0, then A2 =
(a) 0 1
0 0
(b) 0 0
0 0
(c) 0 16
0 0 
(d) 0 4
0 0
3. If A = 3 − 4
1 − 1  then An is
(a) 2n − 4n + 1
n 1 − 2n 
(b) 1 + 2n − 4n
n 1 − 2n 
(c) 1 + 3n − 4n
n 1 + 2n 
(d) 1 + 3n − 4n
n 1 − 2n 
4. If  1 − k 2
3 1 + k  + A=  2 0
0 2  , then A =
(a)  1 − k − 2
−3 1 + k 
(b)  1 + k 2
−3 1 − k 
(c)  1 + k 2
3 1 − k 
(d)  1 + k − 2
−3 1 − k 
5. The matrix  0 6
0 0  is a matrix
(a) Involutary
(b) Nilpotent
(c) Orthogonal
(d) Skew-symmetric
6. The rank of a 3 × 5 matrix in which one row is a constant multiple of the other is lessthan or equal to
(a) 2
(b) 1
(c) 5
(d) 3
7. L U decomposition method fails if lii = uii =
(a) 3
(b) 0
(c) 2
(d) 1
8. The rank of a matrix A = 264
1 2 3
0 x 4
1 − 1 1
375
is 2, then the value of x is
(a) 5
(b) 3
(c) 6
(d) 4
9. The value of x and y, if  0 − 1
1 0   x
y  =  5
4 
(a) x = 4 , y = -5
(b) x = 4 , y = 5
(c) x = 4 , y = 3
(d) x = 1 , y = 2
10. If A is a non singular matrix then the linear system AX = 0 has only
(a) the zero solution
(b) a non-zero solution
(c) infinite solution
(d) unique solution
11. Characteristic equation of A = 24
2 2 − 7
2 1 2
0 1 − 3 35 is
(a) 3+15+12 = 0
(b) 3−13−12 = 0
(c) 3−13+12 = 0
(d) 3−15+12 = 0
12. Eigen values of A =  1 0
3 2  are
(a) 1,2
(b) 2,3
(c) - 1, -2
(d) 0,1
13. If one of the eigen values of A is zero, then A is
(a) singular
(b) skew - symmetric
(c) non-singular
(d) symmetric
14. The normalized eigen vector corresponding to the eigen value  = 2 for the vector ( 2, 1) is
(a) (-2/p5, 1/p5 )
(b) (1/p5, 1/p5 )
(c) (2/ p5, 1/p5 )
(d) (2/p5,−1/p5 )
15. The eigen vector corresponding to the eigen value is
(a) independent
(b) Dependent
(c) not unique
(d) unique
16. The characteristic equation of a square matrix A is 3 − 32 − 7 - 11 = 0, then A−2 =
(a) 1
11[A + 7A−1+3I] = 0
(b) 1
11[A + 7A−1−3I] = 0
(c) 1
11[A − 7A−1+3I] = 0
(d) 1
11[A − 7A−1−3I] = 0
17. If the characteristic equation of the square matrix A is 2 - 4 = 0 then A4 =
( where I is the second order unit matrix )
(a) 16 I
(b) 4 I
(c) I
(d) 64 I
18. The diagonal matrix has the eigen values of A as its elements
(a) positive
(b) diagonal
(c) row
(d) real
19. Given A =  4 1
3 2  , P =  1 1
−3 1  and D =  1 0
0 5  then the value of P−1A4P =
(a)  1 0
0 125 
(b)  1 0
0 25 
(c)  1 0
0 625 
(d)  1 0
0 5 
20. If D is the diagonal matrix with eigen values of A as the principal diagonal elements then D is
(a) spectral matrix
(b) Model matrix
(c) Null matrix
(d) Unit matrix
D B B D B A B C B A C A A C C D A B C A