Let $A=\left[\begin{array}{rr}2 & -2 \\ 4 & 3\end{array}\right]$
$|A|=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]=14 \neq 0$

Since determinant of the matrix is not zero, so inverse of this matrix is possible.

As we know, formula to find matrix inverse is:

$\mathrm{A}^{-1}=\frac{1}{|\mathrm{~A}|} \mathrm{adj} \cdot \mathrm{A}$

adj. $A=\left[\begin{array}{ll}3 & 2 \\ -4 & 2\end{array}\right]$

This implies,

$A^{-1}=\frac{1}{14}\left[\begin{array}{ll}3 & 2 \\ -4 & 2\end{array}\right]$