SOLUTION: proof : A^n is invertible and A^n.-1 = A^-n .

Question 1109397: proof :
A^n is invertible and A^n.-1 = A^-n .
Answer by ikleyn(53765)   (Show Source): You can put this solution on YOUR website!
.
Since your formulation is far from to be perfect, I will edit the formulation:

        Prove:
        If A is invertible matrix, then = .

I will prove it for n = 2, and you will see from there how to do it in the general case.

We are given that   = I.


Then   =  =  =  =  = I.


QED.

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