Answer
$$ \begin{pmatrix}-1&-3\\ \frac{2}{3}&\frac{7}{3}\end{pmatrix}$$
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:
$$\frac{1}{\det \begin{pmatrix}-7&-9\\ 2&3\end{pmatrix}}\begin{pmatrix}3&-\left(-9\right)\\ -2&-7\end{pmatrix} \\ \begin{pmatrix}-1&-3\\ \frac{2}{3}&\frac{7}{3}\end{pmatrix}$$
