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QUESTION
Let A and B be two n x n matrices. Call A and B simultaneously diagonalizable, if there is a single matrix X and two diagonal matrices DA and DB so...
Let A and B be two n x n matrices. Call A and B simultaneously diagonalizable, if there is a single matrix X and two diagonal matrices DA and DB so that A = X-1 DA X and B = X-1 DB X. Show that if A and B are simultaneously diagonalizable, then A and B commute, that is AB = BA.
