60. Show that the matrix C below is tripotent and find its characteristic roots.

$$C = \frac{1}{12} \begin{bmatrix} 1 & 1 & -5 & 3 \\ 1 & 1 & -5 & 3 \\ -5 & -5 & 7 & 3 \\ 3 & 3 & 3 & -9 \end{bmatrix}$$