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If $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 2\end{array}\right], \quad B=\left[\begin{array}{ll}4 & 1 \\ 3 & 1\end{array}\right], \quad$ then $(A+B)^{-1}=$
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$\frac{1}{7}\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]$
$A+B=\left[\begin{array}{ll}1 & 1 \\ 1 & 2\end{array}\right]+\left[\begin{array}{ll}4 & 1 \\ 3 & 1\end{array}\right]=\left[\begin{array}{ll}5 & 2 \\ 4 & 3\end{array}\right]$
$|A+B|=15-8=7$ and adj $(A+B)=\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]$
$\therefore(A+B)^{-1}=\frac{1}{7}\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]$
$|A+B|=15-8=7$ and adj $(A+B)=\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]$
$\therefore(A+B)^{-1}=\frac{1}{7}\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]$
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