Science:Math Exam Resources/Courses/MATH307/December 2006/Question Section 102 07 (b)
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Question Section 102 07 (b)
Decide whether or not the following statement is true or false. If true, give a proof. If false, give a counterexample.
(b) If AB = I, then BA = I. (Warning: do not assume that A and B are square matrices.)
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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The warning in the problem is a hint. Try considering non-square matrices.
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AB = = =
BA = =
If then is not always true.