# Assuming that the system (s,*) has an identity element ,prove that:

1. Nov 2, 2012

### Maths Lover

assuming that the system (s,*) has an identity element. if the equation
(a*b)*(c*d)=(a*c)*(b*d) holds for all a,b,c,d belongs to S ,

,prove that:* is associative and commutative .

I tried so much but with no good result !

any ideas ?

2. Nov 2, 2012

### tiny-tim

Hi Maths Lover!

Try "commutative" first …

put two of a b c or d equal to the identity.

3. Nov 2, 2012

### HallsofIvy

Staff Emeritus
What happens if you take c and d equal to the identity?