If a black hole that originated from a massive star made of anti-matter collided with another black hole that originated from a star made of "ordinary" matter what would happen? Would the black hole made from the anti-matter star retain "anti" properties such that the two black holes would annihilate each other in a brilliant flash of energy or would the merge be the same as any other black hole merge, regardless of the type of matter from which the black hole came?
First, a matter-antimatter collision is 100% efficient. So even if you had a collision on the scale of a 10 million solar mass matter star combining with a 10 million solar mass antimatter star, all of that mass would convert into energy. For example, energy of that sort of collision would go into very high energy gamma rays.
Now, the problem with extending this knowledge to the case of the two black holes you proposed has to do with John Wheeler's "no hair" theory. When a black hole is formed, since no information can leave the black hole due to its intense gravity, there is no way for us to tell what exact process or type of star created the black hole. We can only measure a black hole's mass, electrical charge, and angular momentum. Black holes will look the same to us whether they were created by a strongly magnetized star, a 'bumpy' star, or even a square star. As John Wheeler said, "A black hole has no hair." Thus we can't really talk about a black hole created by a matter star versus a black hole created by an antimatter star, let alone what would happen if they were to collide.
To find out more about black holes, I would recommend Kip Thorne's 'Black Holes and Time Warps: Einstein's Outrageous Legacy.' The book is not too hard but not too easy and has very helpful illustrations.
This page was last updated June 27, 2015.