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rbzima

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**Please HELP!!**

So, I have to go about proving the following, but I have no idea where to even start:

I. Let S = R – {3}. Define a*b = a + b – (ab)/3.

1. Show < S,*> is a binary operation [show closure].

2. Show < S,*> is a group.

3. Find *-inverse of 11/5

II. Let G be a group with x,y contained in G .

Prove: (xy)^2 = x^2 y^2 which implies xy = yx.

xy = yx which implies (xy)^2 = x^2 y^2.

III. Let G be a group with x • x = e , For any x contained in G.

Prove: G is an abelian group.

Honestly, any help would be great because I really have no idea where to even start for any of these!

P.S. - This is not homework, but simply review for a test coming up in Abstract Algebra.

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