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

1. Apr 18, 2013

mahrap

1. Find A, a 2x2 matrix, where $A^{1001}=I_{2}$

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

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

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. Apr 18, 2013

Dick

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

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