Question:
If $A=\left[\begin{array}{cc}1 & 2 \\ 3 & -1\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 0 \\ -1 & 0\end{array}\right]$, find $|A B|$.
Solution:
$A=\left[\begin{array}{ll}1 & 2\end{array}\right.$
$3-1]$
$B=\left[\begin{array}{ll}1 & 0\end{array}\right.$
$\left.\begin{array}{ll}-1 & 0\end{array}\right]$
$A B=\left[\begin{array}{ll}1 & 2\end{array}\right.$
$3-1]\left[\begin{array}{ll}1 & 0\end{array}\right.$
$-1 \quad 0]=\left[\begin{array}{ll}1-2 & 0+0 \\ 3+1 & 0+0\end{array}\right]=\left[\begin{array}{cc}-1 & 0 \\ 4 & 0\end{array}\right]$
$|A B|=0-0=0$
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