Eigenvalues and eigenvectors of A² given A's eigenvalues

[soc4ward14]

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]

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.

 

[soc4ward14]

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

 

[Evo]

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

Thanks!