I have matrix A, how do I find A^n?
I see that the results are repeating after every other multiplications but don't know how to write a general formula. Do I need mathematical induction for this?
You could use induction, but I'd use simpler methods. Once you've established that [imath]A^2=I[/imath] what can you say about [imath]A^{2m}[/imath] for arbitrary [imath]m[/imath]? What about [imath]A^{2m+1}[/imath]?
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