Let * be a binary operation on `Q-{-1}` defined by `a*b=a+b+a b` for all `a ,\ b in Q-{-1}` . Then, Show that every element of `Q-{-1}` is invertible. Also, find the inverse of an arbitrary element.

Explanation

Let `a in Q−{−1}` and `b in Q−{−1}` be the inverse of `a`.

Then,
`a∗b=e=b∗a`

`a∗b=e` and `b∗a=e`

`a+b+ab=0` and `b+a+ba=0`

`b(1+a)=−a in Q−{−1}`

`b=
frac{-a}{1+a}`
...