Let $\displaystyle A=\left[\begin{array}[pos]{cc}

0 & 1 \\

-1 & 0 \\

\end{array}\right]$. Find $\displaystyle A^{1000}$.

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- Dec 12th 2009, 11:37 PMjmedsy[SOLVED] powers of matrices
Let $\displaystyle A=\left[\begin{array}[pos]{cc}

0 & 1 \\

-1 & 0 \\

\end{array}\right]$. Find $\displaystyle A^{1000}$.

- Dec 13th 2009, 12:02 AMjmedsy
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 $\displaystyle A^4$.