Question: Similar Matrices Prove the statements in Problems 1-3 given the following definition? A matrix B is defined to be similar to matrix A (denoted by

Similar Matrices Prove the statements in Problems 1-3 given the following definition?
A matrix B is defined to be similar to matrix A (denoted by B ~ A) if there is an invertible matrix P such that B = P-1 AP?
1. Matrix B is similar to itself; that is, B ~ B.
2. If B ~ A, then A ~ B.
3. lf A ~ B and B ~ C, then A ~ C.

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