Show that the binary operation * on `A=R-{-1}` defined as `a*b=a+b+a b` for all `a ,bA` is commutative and associative on `Adot` Also find the identity element of `*` in `A` and prove that every element of A is invertible.

Explanation

We have `a∗b=a+b+ab` for all `a,b in A`, where `A=R−{−1}`


Commutativity : For any `a,b in R−{−1}`,

To prove: `a∗b=b∗a`

Now, `a∗b=a+b+ab __(1)`

`b∗a=b+a+ab ____(2)`

From (1) and (2), we get
`a∗b=b∗a`
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