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.
Binary Operation is Closed: The only case where it would not be closed is when,Originally Posted by TexasGirl
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,