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

Question

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

Aicharya · Accepted Answer

$\begin{aligned} & A B=\left[\begin{array}{ll}2+1+1 & 3+4+2 \ 6+1+3 & 9+2+6\end{array}ight] \ & =\left[\begin{array}{cc}5 & 9 \ 10 & 17\end{array}ight] \ & (A B)-1=\frac{1}{-5}\left[\begin{array}{cc}17 & -9 \ -10 & 5\end{array}ight]=\left[\begin{array}{cc}-\frac{17}{5} & \frac{9}{5} \ 2 & -1\end{array}ight]\end{aligned}$

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

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