Hi everybody,

f is a binary operation defined in $\displaystyle \mathbb{R}$ as follows:

$\displaystyle (\forall (x,y) \in \mathbb{R}^2) x_* y=xy-2(x+y)+6$

I find that $\displaystyle _*$ is commutative and associative.

I must show that $\displaystyle _*$ takes a neutral element; and i must find if each element of $\displaystyle \mathbb{R}$ has an inverse element?

How to do it??

Thanks.