Answer
The matrices are not inverse of each other.
Work Step by Step
When two matrices are the inverses of each other, then their products must be the identity matrix.
Suppose that matrix- A and matrix-B are having size of $n \times n$ matrix form, then both are inverse of each other when either $AB=I_n$ or $BA=I_n$.
We have $A=\begin{bmatrix} 2 & 1 \\ 3&2 \end{bmatrix}$ and $B=\begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix}$ .
Now,
$AB=\begin{bmatrix} 2 & 1 \\ 3&2 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix} \\=\begin{bmatrix} 4-3 & 2+2 \\ 6-6 & 3+4 \end{bmatrix} \\=\begin{bmatrix} 1 &40 \\ 0&7 \end{bmatrix}$
This shows that $AB \ne I_2$, and the given matrices are not inverse of each other.
