Let `S` be the set of all rational number except 1 and * be defined on `S` by `a*b=a+b-a b ,` for all `a ,bSdot` Prove that (i) * is a binary operation on `( i i ) * is commutative as well as associative.

Explanation

* be defined on `S`
by `a`*`b=a+b-a b`,
for all `a ,b in S`

Then we have to prove that

(i)* is a binary operation on S

Now take `a+b-ab=1`

`a – ab + b – 1 = 0`

`implies a(1 – b) – 1(1 – b) = 0`

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