Question

$A$ and $B$ are two non-zero square matrices such that $AB=0$. Then

• A. Both $A$ and $B$ are singular
• B. Either of them is singular
• C. Neither matrix is singular
• D. None of these

Answer 1

The correct option is B Either of them is singular

Given $AB=0$

$\Rightarrow |AB|=0$

$\Rightarrow |A||B|=0$

$\Rightarrow |A|=0or|B|=0$