If AT = A-1, where A is a real matrix, then A is
A. | normal |
B. | symmetric |
C. | Hermitian |
D. | orthogonal |
Option: D Explanation : |
If A and B are non-zero square matrices, then AB = 0 implies
A. | A and B are orthogonal |
B. | A and B are singular |
C. | B is singular |
D. | A is singular |
Option: A Explanation : |
If A and B be real symmetric matrices of sizen n x n, then
A. | AA^{T} = 1 |
B. | A = A^{-1} |
C. | AB = BA |
D. | (AB)^{T} = BA |
Option: D Explanation : |
If, A, B, C are square matrices of the same order, then (ABC)-1 is equal to
A. | C^{-1}A^{-1}B^{-1} |
B. | C^{-1} B^{-1} A^{-1} |
C. | A^{-1} B^{-1}C^{-1} |
D. | A^{-1} C^{-1} B^{-1} |
Option: B Explanation : |
Consider the following statements
S1: Sum of the two singular n x n matrices may be non-singular
S2 : Sum of two the non-singular nx n matrices may be singular.
Which of the following statements is correct?
A. | S1 and S2 are both true |
B. | S1 is true, S2 is false |
C. | S1 is false, S2 is true |
D. | S1 and S2 are both false |
Option: A Explanation : |