If $A=\left[\begin{array}{cc}2& -6\\ -1& 1\end{array}\right]$  and $B=\left[\begin{array}{cc}-1& 0\\ 1& 2\end{array}\right]$ , then ${\left(A+B\right)}^{-1}$  is

$A+B=\left[\begin{array}{cc}1& -6\\ 0& 3\end{array}\right]$

$adj\left(A+B\right)=\left[\begin{array}{cc}3& 6\\ 0& 1\end{array}\right]$

$\left|A+B\right|=3\times 1-\left(-6\right)\times 0$

$=3+0$

$=3$

${\left(A+B\right)}^{-1}=\frac{1}{\left|A\right|}.adjA$

$=\frac{1}{3}\left[\begin{array}{cc}3& 6\\ 0& 1\end{array}\right]$

$=\left[\begin{array}{cc}1& 2\\ 0& \frac{1}{3}\end{array}\right]$