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- Thread starter AxiomOfChoice
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- #2

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[tex] uv=1[/tex]

If there exists a w such that:

[tex]vw=1[/tex]

Then by associativity:

[tex]w=1w=(uv)w=u(vw)=u1=u[/tex]

Thus if such a w exists it must be u.

This isn't quite enough but I can't find a short proof either. I'll think on it.

- #3

matt grime

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L(a,b,c,d,...) = (b,c,d,....)

R(a,b,c,..)=(0,a,b,c...)

LR=id, and RL=/=id.

You won't find one in 2x2 matrices - the invertible ones form a group, so there's no point looking.

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