Proof of Eigenvalue of A^2 When λ is Eigenvalue of A

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Homework Statement


Let λ be an eigenvalue of A. Then λ^2 is an eigenvalue of A^2




The Attempt at a Solution



I know I have to start by using the fact that λ is an e.v of A then set up an equation relating the eigenvalues and vectors to A which is: Ax=λx. And I understand that the equation for λ^2 and A^2 would be: A^2(x)=λ^2(x)...but i don't know how to prove that :-(
 
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Ax=λx,so AAX=Aλx=λAX=λ*λx,namely A^2(x)=λ^2(x)
 

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