Let K be an algebraically closed filed of characteristic 0 and let G = Z(sub)m x Z(sub)n. We find the conditions under which the elements of the group ring KG are units and idempotents respectively by using the represented matrix. We can see that if $alpha$ = ∑r(g)g $in$ KG is an idempotent then r(1) = 0, 1/mn, 2/mn, …, (mn-1)/mn or 1.