Question:
If $A=\left[\begin{array}{cc}1 & 2 \\ 3 & -1\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -4 \\ 3 & -2\end{array}\right]$, find $|A B|$.
Solution:
$A=\left[\begin{array}{rr}1 & 2 \\ 3 & -1\end{array}\right]$
$\Rightarrow|A|=-1-6=-7$
$B=\left[\begin{array}{cc}1 & -4 \\ 3 & -2\end{array}\right]$
$\Rightarrow|B|=-2+12=10$
If $A$ and $B$ are square matrices of the same order, then $|A B|=|A||B|$.
$\Rightarrow|A B|=|A||B|=-7 \times 10=-70$