Question

prove that any finite semi group is a group if and only if both the cancellation law holds in it​

Answer 1

Step-by-step explanation:

Show that if both cancellation laws i.e w.a=w.b⟹a=b and a.w=b.w⟹a=b holds then a finite semi-group (a finite set with associative binary operation) is a group.

I have seen some proofs which uses the alternative definition of group to prove it i.e. a.x=b and y.a=b have unique solutions for x and y. I am not interested in such proofs.