Let $G$ be the group $ ( \mathscr{M}\_{2\times2}(\mathbb{Q}) , \times ) $ of nonsingular matrices.

Let $ A = \left (
\begin{matrix}
 0 & -1 \\ 
 1 & 0 
\end{matrix}
\right ) $, the order of $A$ is $4$;

Let $ B = \left (
\begin{matrix}
 0 & 1 \\ 
 -1 & -1 
\end{matrix}
\right ) $, the order of $B$ is $3$.

Show that $AB$ has infinite order.

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The only reasoning possible here is by contradiction as $G$ is not abelian. And so I tried, but I got stuck before any concrete development.

Any hints are welcome,
Thanks.