Prove matrix A has same eigenvector as A^2

**Glitch** · September 25th 2011, 04:48 AM

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?

**Deveno** · September 25th 2011, 05:04 AM

Av = λv.

so A^2(v) = A(λv) = λ(Av) = .....?

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Prove matrix A has same eigenvector as A^2

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