Question: Let A, B, and C denote n n matrices. Using only Theorem 4, show that: (a) If A and AB are both invertible, B

Let A, B, and C denote n × n matrices. Using only Theorem 4, show that:
(a) If A and AB are both invertible, B is invertible.
(b) If AB and BA are both invertible, A and B are both invertible.
(c) If A, C, and ABC are all invertible, B is invertible.

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