If $A=\left[\begin{array}{ccc}1 & 2 & 1 \ -1 & 1 & 3\end{array} ight]$ and $B=\left[\begin{array}{cc}1 & 2 \ -3 & 1 \ 0 & 2\end{array} ight]$, then $(A B)^{-1}$

Question

If $A=\left[\begin{array}{ccc}1 & 2 & 1 \ -1 & 1 & 3\end{array}ight]$ and $B=\left[\begin{array}{cc}1 & 2 \ -3 & 1 \ 0 & 2\end{array}ight]$, then $(A B)^{-1}$

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{AB}=\left[\begin{array}{ccc}1 & 2 & 1 \ -1 & 1 & 3\end{array}ight]\left[\begin{array}{cc}1 & 2 \ -3 & 1 \ 0 & 2\end{array}ight] \ & =\left[\begin{array}{cc}1-6+0 & 2+2+2 \ -1-3+0 & -2+1+6\end{array}ight]=\left[\begin{array}{ll}-5 & 6 \ -4 & 5\end{array}ight] \ & 	herefore|\mathrm{AB}|=\left[\begin{array}{cc}5 & -6 \ 4 & -5\end{array}ight] \ & 	herefore(\mathrm{AB})^{-1}=\frac{\left[\begin{array}{cc}5 & -6 \ 4 & -5\end{array}ight]}{(-1)}=\left[\begin{array}{ll}-5 & 6 \ -4 & 5\end{array}ight]\end{aligned}$

If $A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 2…

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