If $A = \begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$, what is $A^{6}$?

Explanation

1. 01

   $A^{2} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} = -I$.

2. 02

   $A^{6} = (A^{2})^{3} = (-I)^{3} = -I$.