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

[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 ?

 

[tiny-tim]

Hi Maths Lover!

Try "commutative" first …

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

 

[HallsofIvy]

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