Question: Let 1, 2, ..., n be a complete set of eigenvalues (repetitions included) of the n n matrix A. Prove that det(A) = 1

Let λ1, λ2, ..., λn be a complete set of eigenvalues (repetitions included) of the n × n matrix A. Prove that
det(A) = λ1 λ2 ··· An and
tr(A) = λ1 + λ2 + ··· + λn

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