Question

If $A$ and $B$ are non - zero square matrices of the same order such that $AB=0$, then

• A. adj $A=0$ or adj $B=0$
• B. adj $A=0$ and adj $B=0$
• C. $|A|=0$ or $|B|=0$
• D. None of these

Answer 1

Answer: (C)

$|A|=0$ or $|B|=0$

From the properties of the matrices, if $A,B$ are non-zero square matrices of same order such that $AB=0$ then the either of the matrices must be singular matrix.

A singular matrix is a matrix whose determinant is zero.

Therefore, $|A|=0$ or $|B|=0$