Chapter 13, Problem 13.9E

Any axis of symmetry $C_n$ that rotates an object by $\theta ={360}^{\text{ο}}/n$ about the z-axis can be generalized by the matrix

$C_n=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0\\ -\sin \theta & \cos \theta & 0\\ 0& 0& 1\end{array}\right]$ (13.18)

(See Table 13.1) Determine the matrix forms of the $C_2\text{, }{C}_3\text{, }{C}_6,$ and $C_1$ rotation operators.