Proving the identity of the field

[playa007]

Homework Statement

If S = {s in R such that s=/=1} is an abelian group under circle operation (Circle Operation a*b = a + b -ab for a, b in R) then R is a field

Homework Equations

The verification of the field axioms

The Attempt at a Solution

The field axiom that I'm struggling to verify is the existence of the identity for the multiplicative operation since s=/=1. I'm wondering if someone can help me resolve this.

Thanks

 

[Dick]

Isn't the identity 0? Why do you think it's not?

 

[HallsofIvy]

If aob= a+ b- ab Then the identity, e, must satisfy a+ e+ ae= a for all a. Solve that for e.