Question
If $A=\left[\begin{array}{ll}2 & 1 \\ 0 & 3\end{array}\right], B=\left[\begin{array}{cc}1 & 2 \\ 3 & -2\end{array}\right]$, verify that $|A B|=|A||| B \mid$.
$|A|=\left|\begin{array}{ll}2 & 1 \\ 0 & 3\end{array}\right|=2(3)-0(1)=6+0=6$
$\begin{aligned} & |B|=\left|\begin{array}{cc}1 & 2 \\ 3 & -2\end{array}\right|=1(-2)-2(3)=-2-6=-8 \\ & |A| \cdot|B|=6(-8)=-48=|A B| \\ & |A B|=|A| \cdot|B|\end{aligned}$
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$\left[\begin{array}{c}5 \\ 4 \\ -3\end{array}\right]$
$\left|\begin{array}{ccc}101 & 102 & 103 \\ 106 & 107 & 108 \\ 1 & 2 & 3\end{array}\right|$
by using properties.