Question

$A$ and $B$ are two non-singular square matrices each of $3\times 3$ such that $AB=A$ and $BA=B$ and $|A+B|\ne 0$, then $|A+B|$ is -

Answer 1

$A^2=A\cdot A=\left(AB\right)A=A\left(BA\right)=AB=A$
Similarily, $B^2=B$
$(A+B{)}^2=A^2+B^2+AB+BA$
$=2(A+B)$
$|A+B{|}^2=8|A+B|\Rightarrow |A+B|=8$