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Math Help - Powers of matrices. Geometric interpretation.

  1. #1
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    Exclamation Powers of matrices. Geometric interpretation.

    Q is in 2x2 matrix form, Q= (0, -1, 1, 0)
    Using geometrical reasoning only, state the smallest possible values of k given that:

    a)Q^-1=Q^k
    Q^-1=Q^3

    b) Q^5=Q^k
    Q^%=Q^1

    c) Q^2=Q^k
    Q^-2=Q^2

    See, I know how to get the answer, I just don't know how to explain it using geometrical reasoning.
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  2. #2
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    Think of Q as a rotation. How many of these rotations are required to get back to where you started? After that, it's just modular arithmetic.
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  3. #3
    MHF Contributor

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    you can also think of Q as a multiplication by a certain complex number. which complex number? well, what is Q^2?
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