Answer
The given matrices are inverses of one another.
Work Step by Step
Matrices are inverses of one another if
$AA^{-1}=A^{-1}A=I_n$
hence
$AA^{-1}=\begin{bmatrix}
2 & -1\\
3 & -1
\end{bmatrix}.\begin{bmatrix}
-1 & 1\\
-3 &2
\end{bmatrix}=\begin{bmatrix}
1 &0\\
0& 1
\end{bmatrix}$
$A^{-1}A=\begin{bmatrix}
-1& 1\\
-3 & 2
\end{bmatrix}.\begin{bmatrix}
2& -1\\
3& -1
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0& 1
\end{bmatrix}$
It shows that the given matrices are inverses of one another.
