Show that a*b=a+b+ab defines a group structure on G=R\{-1} using that 1+a*b=(1+a)(1+b).

not that G=R\{-1} means that G is all real numbers excluding -1.

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- Apr 4th 2006, 06:05 AMTexasGirlGroup Structure
Show that a*b=a+b+ab defines a group structure on G=R\{-1} using that 1+a*b=(1+a)(1+b).

not that G=R\{-1} means that G is all real numbers excluding -1. - Apr 4th 2006, 02:13 PMThePerfectHackerQuote:

Originally Posted by**TexasGirl**

**Binary Operation is Closed**: The only case where it would not be closed is when,

Thus,

Thus,

Thus,

Impossible, thus the binary operation is closed.

**Associative:**We have,

And,

Thus,

**Identity**: We have, that,

and,

.

**Inverse**: Notice that,

Finally, we need to show if, then, the element

Assume, it were then,

Thus,

Thus,

Thus,

Impossible, thus,