You could use the result that any endomorphism whose minimal polynomial has distinct roots is diagonalizable.
Show that a trigonalizable endomorphism p of a finite dimensional vector space V over K=R or K=C, which satisfies (p^k)=Id for some k element of N (excluding zero) is in fact diagonalizable.
Note: an endomorphism is called trigonalizable if it is represented by an upper triangular matrix wrt a suitable basis