Answer
Option C
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:
$$\frac{1}{\det \begin{pmatrix}10&-3\\ 3&-1\end{pmatrix}}\begin{pmatrix}-1&-\left(-3\right)\\ -3&10\end{pmatrix} \\ \begin{pmatrix}1&-3\\ 3&-10\end{pmatrix}$$
