Question: (a) Use the definition for similar matrices (i.e., B ~ A if and only if B = p-1 AP for some invertible matrix P) to

(a) Use the definition for similar matrices (i.e., B ~ A if and only if B = p-1 AP for some invertible matrix P) to show that similar matrices have the same characteristic polynomials and eigenvalues.
(b) Show, using 2 × 2 matrices as examples, that the eigenvectors may be different for similar matrices.

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