# [SOLVED] powers of matrices

• Dec 12th 2009, 11:37 PM
jmedsy
[SOLVED] powers of matrices
Let $A=\left[\begin{array}[pos]{cc}
0 & 1 \\
-1 & 0 \\
\end{array}\right]$
. Find $A^{1000}$.
• Dec 13th 2009, 12:02 AM
jmedsy
nevermind, got it. after looking at the matrix to powers 1 through 5, i can see that $A=A^{4k+1}$ while $k$ is a positive integer. $A^{1000}$ is of the form $A^{4k}$, therefore it is equal to $A^4$.