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Simple order of matrices question...

Find the order of the element
Unparseable latex formula:

\begin{array}{cc}[br]\left(2 & 7\\[br]-1 & -3\right)\]\end{array}[br]

in the group GL(2,R)GL(2,\mathbb{R})


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How would I go about doing this? :hmmmm2:
Original post by RamocitoMorales

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How would I go about doing this? :hmmmm2:


If you call the matrix A, then work out A^2, A^3,.... until you get to I; and pray you don't make an arithmetic slip.
Reply 2
You could just try calcuating powers of the matrix until you hit the identity matrix. The determinant suggests this is a possibility.

A more sophisticated approach would be to consider the eigenvalues of the matrix.

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