a
(a) We have
$F(\alpha )\,F( - \alpha )\, = \,\left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]\,\,\left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{\sin \alpha }&0\\{ - \sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$
= $\left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right] = I$
$\therefore $ $F( - \alpha ) = {[F(\alpha )]^{ - 1}}$.