Unformatted text preview: the inverse map possibly be except left multiplication by a ± 1 ? So let’s try that. We have L a ± 1 .L a .x// D a ± 1 .ax/ D .a ± 1 a/x D ex D x; so L a ± 1 ı L a D id G . A similar computation shows that L a ı L a ± 1 D id G . This shows that L a and L a ± 1 are inverse maps, so both are bijective. The proof for R a is similar. n Corollary 2.1.6. Let G be a group and let a and b be elements of G . The equation ax D b has a unique solution x in G , and likewise the equation xa D b has a unique solution in G ....
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- Fall '08
- Algebra, Inverse relation, map La