If [itex]M[/itex] is a monoid and [itex]u,v\in M[/itex], and [itex]uv = 1[/itex], do we know [itex]vu = 1[/itex]? Can someone prove this or provide a counterexample? I tried to come up with one (a counterexample, that is) using 2 x 2 matrices but was unsuccessful.(adsbygoogle = window.adsbygoogle || []).push({});

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# For a monoid, if uv = 1, do we know vu = 1?

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