Answer
$$\begin{pmatrix}-3&4\\ 4&-5\end{pmatrix}$$
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, we obtain:
$$\frac{1}{\det \begin{pmatrix}5&4\\ 4&3\end{pmatrix}}\begin{pmatrix}3&-4\\ -4&5\end{pmatrix} \\ \begin{pmatrix}-3&4\\ 4&-5\end{pmatrix}$$
