Finding elements in GL_2(R) with specific orders

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Hi,

Is there a way to find elements in ##GL_2(\mathbb{R})## with an arbitrary order other than by trial and error? Suppose I wanted to find ##A\in GL_2(\mathbb{R}):\; o(A)=165##. Is there no methodical way to find this? Is it possible perhaps I can find a product of matricies, each individually relatively easy to determine the order, such that the order of the product is the order I need?

Thanks,
Jack
 
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How about a rotation by an angle of 2\pi/165?
 
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