jika p=Q³ degan Q=[tex] \left[\begin{array}{ccc}1/2&-1/2 \sqrt{3} \\1/2 \sqrt{3} &1/2\end{array}\right] [/tex] , maka p[tex] \left[\begin{array}{ccc}-1\\3\end

[tex]\displaystyle Q=\left[\begin{array}{ccc}\frac12&-\frac12\sqrt3\\\frac12\sqrt3&\frac12\end{array}\right]\\Q^2=\left[\begin{array}{ccc}\frac12&-\frac12\sqrt3\\\frac12\sqrt3&\frac12\end{array}\right]\left[\begin{array}{ccc}\frac12&-\frac12\sqrt3\\\frac12\sqrt3&\frac12\end{array}\right]\\Q^2=\left[\begin{array}{ccc}\frac14-\frac34&-\frac14\sqrt3-\frac14\sqrt3\\\frac14\sqrt3+\frac14\sqrt3&-\frac34+\frac14\end{array}\right][/tex]
[tex]\displaystyle Q^2=\left[\begin{array}{ccc}-\frac12&-\frac12\sqrt3\\\frac12\sqrt3&-\frac12\end{array}\right]\\Q^3=\left[\begin{array}{ccc}-\frac12&-\frac12\sqrt3\\\frac12\sqrt3&-\frac12\end{array}\right]\left[\begin{array}{ccc}\frac12&-\frac12\sqrt3\\\frac12\sqrt3&\frac12\end{array}\right]\\Q^3=\left[\begin{array}{ccc}-\frac14-\frac34&\frac14\sqrt3-\frac14\sqrt3\\\frac14\sqrt3-\frac14\sqrt3&-\frac14-\frac34\end{array}\right][/tex]
[tex]\displaystyle Q^3=\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right]\\Q^3=-I\\P=-I\\\\P\left[\begin{array}{ccc}-1\\3\end{array}\right]=-I\left[\begin{array}{ccc}-1\\3\end{array}\right]\\P\left[\begin{array}{ccc}-1\\3\end{array}\right]=-\left[\begin{array}{ccc}-1\\3\end{array}\right]\\\boxed{\boxed{P\left[\begin{array}{ccc}-1\\3\end{array}\right]=\left[\begin{array}{ccc}1\\-3\end{array}\right]}}[/tex]