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Ok tell me if Im doing it right

a*0=a+0=a
0*a=0+a=a
a*0=0*a=a

0 is the identity element

Looks good so far

You may want to note that in each of those examples, clearly a+0 is less than 6

Yes ,what about the second part ?

Just show that (6-a)*a=a*(6-a)=0 for all a in {0,1,2,3,4,5}

(6-a)*a=6-a+a=6 ? what did i do wrong?

ok 6-a+a-6=0 :)

but how do i know if a+b <6 or a+b≥6

and sorry how is a-6 inverse of a?

yes sorry i meant 6-a

Ok Thank You
I appreciate your help , you deserve a medal ;)

No problem, always glad to help :)