Question: Two matrices A and B are said to be similar, written A ~ B, if there exists an invertible matrix S such that B =

Two matrices A and B are said to be similar, written A ~ B, if there exists an invertible matrix S such that B = S-1 AS. Prove:
(a) A ~ A
(b) If A ~ B, then B ~ A.
(c) If A ~ B ~ C, then A~ C.

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