# Prove that if A has eigenvalues then determinant of A is the product of eigenvalues [duplicate]

How can I prove that if A has eigenvalues then determinant of A is the product of its eigenvalues?

• Look at your the constant in the characteristic polynomial and use the relation between roots of equation and product of roots. – Yadati Kiran Nov 16 '18 at 18:42

2) $$\textrm{det}(AB) = \textrm{det}(A)\textrm{det}(B)$$