Putnam 1984 B3

Prove or disprove the following statement: If $F$ is a finite set with two or more elements, then there exists a binary operation $*$ on $F$ such that for all $x,y,z$ in $F$ , $(\text i)$ $x*z=y*z$ implies $x=y$ $(\text{ii})$ $x*(y*z)\ne(x*y)*z$