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In a group, prove that (ab)^-1=b^-1a^-1. Find an example thats hows that it is possible to have (ab)-2=/=b^-2a^-2 Find distinct monidentity element a and b from a non-Abelian group with the property that (ab)-1=a^-1b^-1. Draw an analogy between the statement (ab)^-1=b^-1a^-1 and the act of putting on and taking off your sock and shoes (shock and shoes property).

 

anyone help pls!

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Hi Dave, i've been done exactly wat you tried to show me above, but my professor mark it wrong, he took my 10 pts out, that's so sad :mad:

 

Here is wat i got:

(ab)^-1=a^-1b^-1 for every a,b are in G

then b^-1a^-1=a^-1b^-1 for every a,b are in G

Mutiplying both side by abon the left: e=aba^-1b^-1

Mutilplying by right: ba=ab since this is true for every a,b are in G, G is Abelian, if G are in Abelien, then (ab)^-1=a^-1b^-1 fore very a,b are in G.

 

give me some hints Dave, thanks a lot

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