Answer
The given matrices are 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: $P=\begin{bmatrix} 2 & 3 \\ 1 & 1 \end{bmatrix}$ and $Q=\begin{bmatrix} -1 & 3 \\ 1 & -2 \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} 2 & 3 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} -1 & 3 \\ 1 & -2 \end{bmatrix}\\ =\begin{bmatrix} (2)(-1) +(3)(1) & (2)(3) +(3)(-2) \\ (1)(-1) +(1)(1)& (1)(3) +(1)(-2) \end{bmatrix} \\\\=\begin{bmatrix} 1 & 0 \\ 0& 1 \end{bmatrix} $
This implies that the given matrices are inverses of each other because $PQ= I_2$, that is, their products show an identity matrix.
