Blood typing test?

Blood that is the same type (A, B, AB, O) should not agglutinate; that is why it is safest to transfuse someone the same type of blood they are. However, there are other antigens and antibodies beyond ABO and Rh. It is possible that there will be a reaction within blood samples of the same type if they have non compatible antigen/antibody components. I would double check your textbook to make sure you are reading it correctly and then clarify with your instructor- are you sure the book doesn't refer to agglutination between antibodies and antigens when they are the same? A trick I learned in school was RABs attack DANs- recipient antibodies (those in the plasma) attack donor antigens (those attached to the RBC). So if you have someone who has type O- blood, they have no antigens attached to the RBC and A, B, and Rh antibodies in the plasma. If you give them type A, B, or AB blood or any Rh+ blood, those antibodies will attack the A, B, and Rh antigens on the donor RBCs.

The fact that type O- blood has no antigens attached to the RBC is why type O- is the universal donor- there are absolutely no antigens attached to the RBC to be attacked by the recipient's antibodies, regardless of ABO and Rh type of the recipient. It's also why type O- patients can only receive type O- blood- they have A, B, and Rh antibodies in the plasma that will attack any other RBC with ABO or Rh antigens.