If i*j*k=i*i=j*j=k*k=-1 then it is easy to demonstrate the lack of commutativity:

(i*j*k)*(i*j*k)=1 but (i*i)*(j*j)*(k*k)=-1

QED

So what are the formulae for l,m,n,&p which so obviously defy associativity?