If $A=\left[\begin{array}{cc}2& 3\\ 5& -2\end{array}\right]$, write $A^{-1}$ in terms of A. 

$|A|=\left|\begin{array}{cc}2& 3\\ 5& -2\end{array}\right|$

$-4-15=-19\ne 0$

Now, $C_{11}=-2,C_{12}=-5,C_{21}=-3and{C}_{22}=2$

$adjA={\left[\begin{array}{cc}-2& -5\\ -3& 2\end{array}\right]}^T$
$=\left[\begin{array}{cc}-2& -3\\ -5& 2\end{array}\right]$

$A^{-1}=\frac{1}{A}adjA$
$=\frac{1}{-19}\left[\begin{array}{cc}-2& -3\\ -5& 2\end{array}\right]$
$=\frac{1}{19}\left[\begin{array}{cc}2& 3\\ 5& -2\end{array}\right]$
$=\frac{1}{19}A$