Answer
$$\begin{pmatrix}-\frac{4}{3}&-3\\ 1&2\end{pmatrix}$$
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, we obtain:
$$\frac{1}{\det \begin{pmatrix}6&9\\ -3&-4\end{pmatrix}}\begin{pmatrix}-4&-9\\ -\left(-3\right)&6\end{pmatrix} \\ \begin{pmatrix}-\frac{4}{3}&-3\\ 1&2\end{pmatrix}$$
