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Thread: [SOLVED] powers of matrices

  1. #1
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    [SOLVED] powers of matrices

    Let $\displaystyle A=\left[\begin{array}[pos]{cc}
    0 & 1 \\
    -1 & 0 \\
    \end{array}\right]$. Find $\displaystyle A^{1000}$.
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  2. #2
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    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 $\displaystyle A^4$.
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