Let (X, *) be a semigroup. Furthermore, for every a and b in X, if a ≠ b, then a*b ≠ b*a.

Based on the defined seimigroup, choose the correct equalities from the options given below:

A. For every a in X, a*a = a

B. For every a, b in X, a*b *a= a

C. For every a, b, c in X, a*b *c= a*c