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:

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

Updated On: Jan 6, 2025

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

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The Correct Option is D

Solution and Explanation

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.

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