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

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

> A^(-1).B.A;

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

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

>