Question

Let A be an n x n matrix, and suppose A has n real eigenvalues, lamda1, ..., lamdan, repeated according to multiplcities so that det(A - lamda Identity) = (lamda1 - lamda)(lamda2 - lamda) ...(lamdan - lamda). Explain why det A is the product of the n eigenvalues of A. (This result is true for any square matrix) when complex eignevalues are considered).