So lets say you have a matrice that has a det of 0 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 .