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

Maths Lover · Nov 2, 2012

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 · Nov 2, 2012

Hi Maths Lover!

Try "commutative" first …

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

HallsofIvy · Nov 2, 2012

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

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

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

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