(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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}.

2. Relevant equations

the operation * is defined by x*y = x + y + xy.

3. 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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Can commutativity of multiplication and addition under real numbers be assumed?

**Physics Forums | Science Articles, Homework Help, Discussion**