If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.

Let A & B be non-singular matrices of order n.

$|A| \neq 0$ and $|B| \neq 0 \quad$ [By definition]

Since they are of same order,

$\begin{aligned}|A B| &=|A||B| \\|A B| &=0 \text { iff either }|A|=0 \text { or }|B|=\end{aligned}$ $=0$

But it is not the case here. Thus, $|A B|$ is non-zero and $A B$ is non-singular matrix.