in case i did not show enough of an attempt at a solution, here is a more detailed attempt summary...
the operation * is commutative if for every x,y∈{x∈R:x≠ -1} such that x*y = y*x.
But, x*y = x + y + xy, and
y*x = y + x + yx,
= y + x + xy (by commutative law of...
Homework Statement
so.. let the operation * be defined as x*y = x + y + xy for every x,y ∈ S,
where S = {x ∈ R : x ≠ -1}. Now i have proven associativity, existence of an identity and inverses, all without commutativity, but i must show that this is an abelian group, so now i have to show...