Proof by induction question. Need some help please?

Posted on 2016-02-17 18:42:00 in Math by CHIRANTHA

"A" and "U" are square matrices, and X=U^-1 AU. Use mathematical induction to prove that X^n = U^-1 A^n U , for n is any real number. 

I went as far as proving that the above formula is true for when n=1 and if the formula is true for "k" then it must be true for "k+1". I just don't know how to prove that it must be true for "k+1". 

Could any one of you smart people please help me out here? 

As always , I will reward maximum points for the best answer ;)

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