I've been learning about matrices and the identity matrix $I$. It says when $AB = BA = I$, then $A$ and $B$ are inverses of one another. Is it possible for $AB$ to equal $BA$ but not equal $I$?
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5Yes, take $A=B$. Or any $A$ and $B=0$. – Clement C. Nov 28 '15 at 14:38
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Yes. Take $B = 0_{n \times n}$. This is always true for two diagonal matrices, and may be true for others. The diagonal case is the simplest to cook examples out of. – stochasticboy321 Nov 28 '15 at 14:40
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2Any power of $A$ will commute with any other power of $A$. – paw88789 Nov 28 '15 at 14:41
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@ClementC. Of course! That makes the most sense, thanks (I can't upvote your answer yet) – user99705 Nov 28 '15 at 14:52
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@ClementC. Mind posting your comment as an answer so the question leaves the unanswered question list? – Peter Woolfitt Nov 28 '15 at 15:01
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As per the comment above: it is possible. Simple examples can be obtained by choosing $A=B$, or $B=0$.
Clement C.
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