Question: We have defined matrix B to be similar to matrix A (denoted by B ~ A) if there is an invertible matrix P such that

We have defined matrix B to be similar to matrix A (denoted by B ~ A) if there is an invertible matrix P such that B = P-1AP. Prove the following:
(a) Similar matrices have the same determinant and the same trace
(b) Show by example (using 2 × 2 matrices) that similar matrices can have different eigenvectors.

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