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## Homework Statement

If A is a symmetric matrix, what can you say about the definiteness of A^2? Explain.

## Homework Equations

I believe I need to use the face that A^2=SD^2S^-1.

I know that if all the eigenvalues of a symmetric matrix are positive then the matrix is positive definiteness and if the eigenvalues are positive and zero then the matrix is semidefinite.

Not sure where to go from here.