Let A and B be similar matrices, so B = S-l A S for some nonsingular matrix S.
(a) Prove that A and B have the same characteristic polynomial: pB(λ) = pA(λ).
(b) Explain why similar matrices have the same eigenvalues. Do they have the same eigenvectors? If not, how are their eigenvectors related?
(c) Prove that the converse is not true by showing that

have the same eigenvalues, but are not similar.

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