The matrix P that multiplies (x, y, z) to give (z, x, y) is also a rotation matrix. Find P and P^3. The rotation axis a = (1, 1, 1) doesn't move, it equals Pa. What is the angle of rotation from v = (2, 3, -5) to Pv = (-5, 2, 3)?

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So far, I've found
\[P = \left[\begin{matrix}0 & 0&1 \\1&0&0\\0&1&0\end{matrix}\right], P ^{3} = I\]

Sorry, for exp(+/- 2 pi/3) read exp(+/- 2 i pi/3)

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