> restart;

> A:=Matrix([[a,b],[c,d]]);

> B:=Matrix([[p,q],[r,s]]);

> (A.B-B.A).(A.B-B.A);

> expand(((b*r-c*q)^2+(a*q+b*s-p*b-q*d)*(c*p+d*r-r*a-s*c))-((a*q+b*s-p*b-q*d)*(c*p+d*r-r*a-s*c)+(c*q-b*r)^2));

> expand((b*r-c*q)*(a*q+b*s-p*b-q*d)+(a*q+b*s-p*b-q*d)*(c*q-b*r));

> expand((c*p+d*r-r*a-s*c)*(b*r-c*q)+(c*q-b*r)*(c*p+d*r-r*a-s*c));

>