Question
Find $|A B|,$ if $A=\left[\begin{array}{cc}0 & -1 \\ 0 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right].$
✓
Answer
Given, $A=\left[\begin{array}{cc}0 & -1 \\ 0 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right]$
$\therefore \quad A B=\left[\begin{array}{cc}0 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right]$
$\text{or}\quad A B=\left[\begin{array}{ll}0+0 & 0+0 \\ 0+0 & 0+0\end{array}\right]$
$\text{or}\quad A B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]=0$
Hence, $|AB|=0$
$\therefore \quad A B=\left[\begin{array}{cc}0 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{ll}3 & 5 \\ 0 & 0\end{array}\right]$
$\text{or}\quad A B=\left[\begin{array}{ll}0+0 & 0+0 \\ 0+0 & 0+0\end{array}\right]$
$\text{or}\quad A B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]=0$
Hence, $|AB|=0$
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