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I'm kind of stuck with this theorem stating that: if A is an unipotent matrix, then exp(log A) = A and also if X is nilpotent then log(exp X) = X

Does anyone know any good approaches to prove this?

I know that for unipotent A, logA will be nilpotent and that for nilpotent X, exp(X) will be unipotent

Thanks!