Doesn't the example show that

    (ii): e1□e2 = -e2□e1

and

    (iii): (e1□e2)□e3 = e1□(e2□e3)

contradict each other? In the end we end up with

    (e1□e3)□e5 = e5□(e1□e3) 

which seems to go against (ii)