# Prove matrix A has same eigenvector as A^2

• September 25th 2011, 05:48 AM
Glitch
Prove matrix A has same eigenvector as A^2
The question
If A is a matrix with eigenvector v and corresponding eigenvalue $\lambda$ prove that v is also an eigenvector of $A^2$ and find the corresponding eigenvalue.

I'm not sure how to attempt this. Any hints?
• September 25th 2011, 06:04 AM
Deveno
Re: Prove matrix A has same eigenvector as A^2
Av = λv.

so A^2(v) = A(λv) = λ(Av) = .....?