Let $\displaystyle R(\theta)=\left[\begin{array}{cc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array}\right]$ denote the 2x2 rotation matrix.

Show that $\displaystyle R(\theta)R(\phi)=R(\theta+\phi)$

Without further matrix calculation, explain why $\displaystyle R(\phi)R(\theta)=R(\theta)R(\phi)$

Anyone willing to help explain how to work this out?