Question

If the product of two non zero square matrices A and B of the same order is a zero matrix then:

• A. Both are singular
• B. Atleast one of A or B is singular
• C. A is non-singular, but B is singular
• D. A is singular but B is non-singular

Answer 1

Answer: (B)

Atleast one of A or B is singular

we have
$det\left(AB\right)=det\left(A\right)det\left(B\right)$
given $AB=0$
therefore,
$det\left(A\right)det\left(B\right)=0$
implies atleast one of A&B is singular