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So X= [1 1; 1 1]

So using some verification and algebra u arive at

X^n= 2^(n-1)[1 1; 1 1]

So I am trying to define what n can be.

I already established n cannot be a - since one would get infinity for an answer since it is a singular matrix.

Another limiation is 0. Since that just gives you an identity which the formula cannot express.

But I am confused with fractions.

Technically they should work but I do not know how to explain it.

Same with irrational numbers.

so can n=1/2?

and if that is not hard enough what about imaginary numbers?????????

For some reason I know they work with non singular matrices .