Define a binary operation on s by a*b=a+b+ab
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I believe you meant to write S=R∖{−1}
0 is indeed the identity element since for any a∈S, a∗0=a+0+a.0=a
For b to be the inverse of a, we require a∗b=0.
Hence a+b+a.b=0
b+a.b=−a
b(1+a)=−a
b=−a1+a
which is fine, since a can't be −1 (since it's not an element of S).
0 is indeed the identity element since for any a∈S, a∗0=a+0+a.0=a
For b to be the inverse of a, we require a∗b=0.
Hence a+b+a.b=0
b+a.b=−a
b(1+a)=−a
b=−a1+a
which is fine, since a can't be −1 (since it's not an element of S).
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