Let A be an n times n matrix, and suppose A has n real eigenvalues, lambda_1, ..., lambda_n, repeated according to multiplicities, so that det (A - lambda I) = (lambda_1 - lambda) (lambda_2 - lambda) (lambda_n - lambda) Explain why det A is the product of the n eigenvalues of A. (This result is true for any square matrix when complex eigenvalues are considered.)