Answer
The given matrices are ${NOT}$ inverses of each other.
Work Step by Step
We know that when two matrices will be inverses of each other, then their products are called as the identity matrix $(I)$.
Suppose $P$ and $Q$ consist of $n \times n$ matrix form, then $P$ and $Q$ are inverse of each other if $PQ=I_n$ and $QP=I_n$
Here, we have: $P=\begin{bmatrix} -1 & 2 \\ 3 & -5 \end{bmatrix}$ and $Q=\begin{bmatrix} -5 & -2 \\ -3 & -1 \end{bmatrix} $ .
As we can see that both matrices of the same dimensions, that is, $2 \times 2$ or, n=2. Thus, we can multiply them easily.
$PQ=\begin{bmatrix} -1 & 2 \\ 3 & -5 \end{bmatrix} \begin{bmatrix} -5 & -2 \\ -3 & -1 \end{bmatrix}$
Using multiplication method, it follows that
$PQ =\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} $
This implies that the given matrices are ${NOT}$ inverses of each other because $PQ \neq I_2$, that is, their products does not show an identity matrix.
