\begin{eqnarray*} && R(-\alpha)R(\alpha) \\ &=& \left( \begin{array}{cc} \cos (-\alpha) & - \sin (-\alpha)\\ \sin (-\alpha) & \cos (-\alpha) \end{array} \right) \left( \begin{array}{cc} \cos \alpha & - \sin \alpha\\ \sin \alpha & \cos \alpha \end{array} \right)\\ &=& \left( \begin{array}{cc} \cos (-\alpha) \cos \alpha - \sin (-\alpha) \sin \alpha & - \sin (-\alpha) \cos \alpha - \cos (-\alpha) \sin \alpha\\ \sin (-\alpha) \cos \alpha + \cos (-\alpha) \sin \alpha & \cos (-\alpha) \cos \alpha - \sin (-\alpha) \sin \alpha \end{array} \right)\\ &=& \left( \begin{array}{cc} \cos 0 & - \sin 0 \\ \sin 0  & \cos 0 \end{array} \right)\\ &=& \left( \begin{array}{cc} 1 & 0 \\ 0  & 1 \end{array} \right)\\ &=& I \end{eqnarray*}