Answer
$\begin{bmatrix}
1&-\frac{5}{2}\\
-1&3
\end{bmatrix}$
Work Step by Step
Using the formula,
$A^{-1} = \frac{1}{|A|}\times{Adj(A)}$
$where, A = \begin{bmatrix} 6&5\\2&2\end{bmatrix}$
$Adj(A) = \begin{bmatrix}d&-b\\-c&a\end{bmatrix}, if A = \begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\implies A^{-1} = \frac{1}{(6)(2)-(2)(5)}\times\begin{bmatrix} 2&-5\\-2&6\end{bmatrix}\\
\quad=\frac{1}{2}\times\begin{bmatrix} 2&-5\\-2&6\end{bmatrix} = \begin{bmatrix}
1&-\frac{5}{2}\\
-1&3
\end{bmatrix}$
