I known that the Smith normal form of $A$ provides two unimodular matrices $U$ and $V$ of respective dimensions $m \times m$ and $n \times n$ such that the matrix $$B=[b_{i,j}]=UAV$$ and B has the form \begin{pmatrix} b_{11} & 0 & \ldots & 0 & 0 & 0 & 0\\ 0 & b_{22} & \ldots & 0 & 0 & 0 & 0\\ \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots\\ \vdots & 0 & \ldots & b_{ii} & \vdots & \vdots & \vdots\\ \vdots & \vdots & \ldots & 0 & 0 & 0 & 0\\ \vdots & \vdots & & \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & \ldots & 0 & 0 & 0 & 0\\ \end{pmatrix}
But I don't know how to find the matrices $U$ and $V$.
For example with the matrix
$$A:= \begin{pmatrix}
3 & 4 \\
2 & 5 \\
-2 & -3
\end{pmatrix}$$
How can I find the matrices $U$ and $V$ to conclude the Smith normal form?