- #1

lostinmath08

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**Associative Law...help please..thanks!**

b1. Homework Statement [/b]

On the set of real numbers R, the following is defined *:RxR arrow R

(x,y) arrow x*y=

**a**(x+y)-xy

find all the values of the real parameter

**a**such that the operation is associative

## Homework Equations

associative law states x*(y*z)=(x*y)*z

## The Attempt at a Solution

x*y = a (x+y) - xy = ax + ay - xy

(m*n) * o = m * (n*o)

(am + an - mn) * o = m * (an + ao - no)

a(am + an - mn) + ao - o (am + an - mn) = am + a (an + ao - no) - m (an + ao - no)

aam + aan - amn + ao - amo - ano + mno = am + aan + aao - ano - amn - amo + mno

am + o = m + ao

am - ao = m - o

a (m - o) = m - o

a = 1 if m does not equal o, and a does not equal 0 if m = 0

im unsure of my solution...any help would be awesome!