Answer
$$\begin{pmatrix}-\frac{1}{12}&\frac{1}{6}\\ -\frac{1}{60}&\frac{1}{15}\end{pmatrix}$$
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:
$$\frac{1}{\det \begin{pmatrix}-24&60\\ -6&30\end{pmatrix}}\begin{pmatrix}30&-60\\ -\left(-6\right)&-24\end{pmatrix} \\ \begin{pmatrix}-\frac{1}{12}&\frac{1}{6}\\ -\frac{1}{60}&\frac{1}{15}\end{pmatrix}$$
