$A B=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]\left[\begin{array}{cc}\cos \beta & -\sin \beta \\ \sin \beta & \cos \beta\end{array}\right]$
Clearly,
$=\left[\begin{array}{cc}\cos (\alpha+\beta) & -\sin (\alpha+\beta) \\ \sin (\alpha+\beta) & \cos (\alpha+\beta)\end{array}\right]=B A \quad$ (verify by using trigonometric properties).