Answer
$$\begin{pmatrix}-\frac{1}{2}&-\frac{5}{12}\\ 2&\frac{2}{3}\end{pmatrix}$$
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:
$$\frac{1}{\det \begin{pmatrix}\frac{4}{3}&\frac{5}{6}\\ -4&-1\end{pmatrix}}\begin{pmatrix}-1&-\frac{5}{6}\\ -\left(-4\right)&\frac{4}{3}\end{pmatrix} \\ \begin{pmatrix}-\frac{1}{2}&-\frac{5}{12}\\ 2&\frac{2}{3}\end{pmatrix}$$
