> e1:=a*c-b*d=1;
                               e1 := a c - b d = 1

> e2:=a*d+b*c=0;
                               e2 := a d + b c = 0

> solve({e1,e2},{d,c});
                                     b            a
                           {d = - -------, c = -------}
                                   2    2       2    2
                                  b  + a       b  + a