# Thread: Prove matrix A has same eigenvector as A^2

1. ## 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?

2. ## Re: Prove matrix A has same eigenvector as A^2

Av = λv.

so A^2(v) = A(λv) = λ(Av) = .....?