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

> T:=Matrix([[1,0],[1,1]]);

> S^(-1).T.S;

> expand((d/(a*d-b*c)-b/(a*d-b*c))*b-b*d/(a*d-b*c));

> expand((-c/(a*d-b*c)+a/(a*d-b*c))*a+a*c/(a*d-b*c));

>