Blood grouping is an antigen-antibody reaction, antigens on the red cells reaction with antibodies in the serum or monoclonal antibodies and vice versa, therefore, people with blood group A have antigen A on their red cells have corresponding Antibody B in their serum whiles those with blood group B have Antigen B on their red cells have corresponding Antibody A in their serum.
Therefore only people with antigen B on their red cells will be able to agglutinate antibody A, the blood group of the person is BLOOD GROUP A.