Prove that if A has eigenvalues then determinant of A is the product of eigenvalues

Question

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

score 0 · Answer 1 · answered Nov 16 '18 at 18:38

0

Hints:

1) Jordan Canonical Form

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

answered Nov 16 '18 at 18:38

BaronVT

1 Answers1