Let A and B be n × n matrices. Suppose it is known that

Chapter 3, Problem 55P

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QUESTION:

Let A and B be n × n matrices. Suppose it is known that either AB = I or BA = I. Use the result of to conclude that B = A?1. Deduce from Theorems 2 and 3 that if A and B are a n × n invertible matrices, then AB is invertible if and only if both A and B are invertible.

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QUESTION:

Let A and B be n × n matrices. Suppose it is known that either AB = I or BA = I. Use the result of to conclude that B = A?1. Deduce from Theorems 2 and 3 that if A and B are a n × n invertible matrices, then AB is invertible if and only if both A and B are invertible.

ANSWER:

Solution:Step 1 of 2:In this problem, we need to conclude that

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