Let a be an n x n matrix and suppose a has n real

Question

Question: Let A be an n X n matrix, and suppose A has n real eigenvalues, λ1,,,,,,,,, λn, repeated according to multiplicities, so that

det (A - λI) = (λ₁ - λ) (λ₂ - λ). . .(λ_n - λ)

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.)