Question

If $A$ and $B$ are any two matrices such that $AB=0$ and $A$ is non-singular, then

• A. $B=0$
• B. $B$ is singular
• C. $B$ is non-singular
• D. $B=A$

Answer 1

The correct option is B $B$ is singular

$A$ is non-singular $\Rightarrow |A|\ne 0$
Given that $AB=0$, taking determinants on both sides, we have

$|A.B|=0$

$\therefore |A|\times |B|=0$

Product of two numbers is zero if and only if one of them is zero.

Since $A$ is non-singular matrix, $B$ has to be singular, meaning that its determinant has to be zero.

The matrix need not be zero.