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Definition: Two n x n matrices A and B are said to be similar if...

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Definition: Two n x n matrices A and B are said to be similar if there exists an invertible n x n matrix P such that A = PBP-. Let A, B and C be arbitrary n x n matrices. If A and B are similar and B and C are similar, prove that A and C are also similar. In your proof, you must explicitly state any properties or theorems you have used.

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Definition: Two n x n matrices A and B are said to be similar if there exists an invertible n x n matrix P such that A = PBP-. Let A, B and C be arbitrary n x n matrices. If A and B are similar and B and C are similar, prove that A and C are also similar. In your proof, you must explicitly state any properties or theorems you have used.

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