Let A be an n x n matrix with eigenvalue $$\lambda$$ . Prove that $$\lambda$$ ^2 is and eigenvalue of A^2 and that if v is an eigenvector for A, then v is also an eigenvector for A^2.

Fredrik
Staff Emeritus
Gold Member
Do you understand what it means for $\lambda$ to be an eigenvalue of A? Just write down what it means, and you're almost done.

I know that Av= $$\lambda$$v but I do not know where to go from that.

Evo
Mentor
I see that you have reposted in the appropriate Homework forum.

Thanks!