Let $\displaystyle A=\left[\begin{array}[pos]{cc}
0 & 1 \\
-1 & 0 \\
\end{array}\right]$. Find $\displaystyle A^{1000}$.
nevermind, got it. after looking at the matrix to powers 1 through 5, i can see that $\displaystyle A=A^{4k+1}$ while $\displaystyle k$ is a positive integer. $\displaystyle A^{1000}$ is of the form $\displaystyle A^{4k}$, therefore it is equal to $\displaystyle A^4$.