The three serums used for blood typing contain antibodies against the A, B and D antigens that code for the different blood types and subtypes. See the link:
It follows that is the Anti-A serum causes agglutination, the blood cells carry the A antigen, making the blood group A.
Similarly, if the Anti-D serum causes agglutination, the blood cells carry the D antigen, making the blood group Rh positive.
See this link for more details: