The consensus opinion of physicists is that antimatter has mass, and it is attracted to other massive objects by gravity in exactly the same way as matter: Antimatter isn't anti-gravity.
Proving this is difficult. It is hard to obtain enough antimatter in one place to observe any gravitational interactions. The best observations aren't even able to conclusively show that antimatter "falls" in a gravitational field. However for theoretical reasons it is considered extremely likely. If antimatter were repulsed by matter, it would allow for violations of the conservation of energy.
A black hole is a region of extreme gravity, and a black-hole would attract matter in just the same way as it attracts antimatter. It would even be possible for antimatter to form a black hole. In fact there are only 11 numbers that define a black hole: mass (made of either matter, antimatter, or energy), position, velocity, spin rate and direction, and electrical charge.
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