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Homework Help: Linear Algebra: Find A for a 2x2 matrix and when A^1001 = I

  1. Apr 18, 2013 #1
    1. Find A, a 2x2 matrix, where [itex]A^{1001}=I_{2}[/itex]

    2. I know that that if [itex]A^{2}=I_{2}[/itex], then A is either a reflection or a rotation by π.

    3. If I use advantage of that fact that A in [itex]A^{2}=I_{2}[/itex] is a rotation by π then I know that [itex]A^{1001}=I_{2}[/itex] is true when A is a rotation by [itex]2π/1001[/itex]

    Is there any other way to do this problem or is it only solvable by considering the fact that A is a rotation. Can you do it by considering A to be a reflection?
  2. jcsd
  3. Apr 18, 2013 #2


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    You said it yourself. A reflection satisfies A^2=I. How can one satisfy A^1001=I?
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