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Math Help - [SOLVED] powers of matrices

  1. #1
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    [SOLVED] powers of matrices

    Let A=\left[\begin{array}[pos]{cc}<br />
      0 & 1 \\<br />
    -1 & 0 \\<br />
\end{array}\right]. Find 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 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.
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