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

Last updated: 8/13/2022

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-¹. 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.