Groups and the Group Axioms · Challenge problem

Real matrices of the form $\begin{pmatrix}a&-b\\b&a\end{pmatrix}$, not both $a,b$ zero, form an abelian group under multiplication. For $A=\begin{pmatrix}1&-2\\2&1\end{pmatrix}$ and $B=\begin{pmatrix}3&-1\\1&3\end{pmatrix}$, find the bottom-left entry of $AB$.