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**limpfisch****Member**- Registered: 2012-05-08
- Posts: 11

let a,b be members of a group (G,*). Show that if (a*b) inverse = (a inverse)*(b inverse) then a*b = b*a

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

hi limpfisch

For simplification I'll leave out the * (say, multiply), use I for the identity and -1 for an inverse

multiply both sides by ab

Now multiply both sides by ba

Bob

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