Why does Anti-A antibodies make type-A blood type clump?
When an antibody meets its antigen it will bind it. So if you add anti-A antibodies to A blood, these antibodies will bind the red blood cells. Because of its Y-shaped form, each antibody can bind two epitopes. These can be located on the same red blood cell, or on two different. If they are located on two different, this leads to cross-linking of two blood cells. Since this happens many times, the blood cells will clump. The whole process is called hemagglutination.

See the image (from here) for illustration: