- #1
sapnpf6
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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 commutativity. I know that multiplication is not always commutative, but i am not using matrices, just reals/{-1}.
Homework Equations
the operation * is defined by x*y = x + y + xy.
The Attempt at a Solution
i simply say that first, addition is commutative on the reals, so x+y=y+x, by the commutative law of addition of real numbers, and second that xy=yx, by the commutative law of multiplication of real numbers. this would show that x*y=y*x. Is this allowed or do i have to show commutativity without assuming addition and multiplication are commutative on real numbers? and if i have to show commutative without the assumptions above, can someone point me in the right direction on the proof?