Proving detA = λ1...λn for Real Eigenvalues

[dsyh]

Homework Statement

Let A be nxn matrix, suppose n has real eigenvalues,λ1,...,λn, repeated according to multipilicities. Prove that detA = λ1...λn.

Homework Equations

The Attempt at a Solution

I started by applying the definition, Av = λv, where v is an eigenvector. then I just dun know how to keep going.. is there anyone can help me out? or at least give me some hints..
thx..

 

[D H]

If matrices A and B are similar, what can you say about their determinants? Use this relationship to help you solve the problem.

 

[kof9595995]

DH offered an correct approach,but you need to know something about similarity and Jordan normal form or Schur's lemma
Here's another approach: consider the characteristic polynomial det(A-λI),by fundamental theorem of algebra, it can be factorized into (λ1-λ)(λ2-λ)...(λn-λ),then let λ=0 and see what will happen