Question

Let P and Q be two matrices such that P Q = 0 and P is non-singular, then
(a) Q is also non-singular
(b) Q = 0
(c) Q is singular
(d) P = Q
Choose the correct answer from the options given below:

• A. (A). (B) and (D) only.
• B. (B) and (C) only.
• C. (A) and (D) only.
• D. (C) only

Hint:

If a non-singular matrix multiplied by another matrix results in the zero matrix the second matrix must be singular

Answer 1

The Correct Option is D

Since P is non-singular and P Q = 0, the matrix Q must be singular. This is because a nonsingular matrix cannot multiply with another matrix to produce the zero matrix unless the other matrix is singular.