Question

If $A=\left[\begin{array}{cc}1& 2\\ 1& 3\end{array}\right]$, then find $A^{-1}+A$.

Answer 1

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

$A^{-1}=\left[\begin{array}{cc}3& -2\\ -1& 1\end{array}\right]$

Therefore,

$A^{-1}+A=\left[\begin{array}{cc}4& 0\\ 0& 4\end{array}\right]=4I$