Answer
$$\begin{pmatrix}4&-3\\ 3&-2\end{pmatrix}$$
Work Step by Step
We know the following equation for the inverse of a matrix:
$$\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$$
Thus:
$$\frac{1}{\det \begin{pmatrix}-2&3\\ -3&4\end{pmatrix}}\begin{pmatrix}4&-3\\ -\left(-3\right)&-2\end{pmatrix} \\ \begin{pmatrix}4&-3\\ 3&-2\end{pmatrix}$$
