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

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

> A^2;

> B^2;

> A^3;

> A.B;

> B.A;

> A.B-B.A; (AB¤£µ¥ó

> A+B;

> Trace(A+B);

> with(linalg);

Warning, the protected names norm and trace have been redefined and unprotected

> trace(A+B);

> trace(A.B);

> trace(B.A);

> A;

> B;

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

> 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));

(AB-BA)(AB-BA) is scalar

>