The nature of the matter-energy within a black hole is not just unknown in practice, but unknowable in theory. Matter particles, antimatter particles, and particles like photons that are neither matter nor antimatter, all have mass-energy and mass-energy is conserved in a merger of black holes.
Interactions of black hole with the world beyond the event-horizon and its properties are purely a function of the total amount of mass-energy within the event horizon and its angular momentum (and also its electromagnetic charge in the purely hypothetical possibility of a black hole with electric charge).
It is worth restating
the basics:
The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as
Schwarzschild black holes after Karl Schwarzschild who discovered this
solution in 1916. According to
Birkhoff's theorem, it is the only
vacuum solution that is
spherically symmetric. This means that
there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.
Solutions describing more general black holes also exist. Non-rotating
charged black holes are described by the
Reissner–Nordström metric, while the
Kerr metric describes a non-charged
rotating black hole. The most general
stationary black hole solution known is the
Kerr–Newman metric, which describes a black hole with both charge and angular momentum. . . .
Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects.
Thus,
Schwarzschild and
Kerr black holes have purely gravitational interactions and properties characterized solely by total mass-energy and in the case of Kerr black holes, angular momentum, while
Reissner–Nordström and
Kerr–Newman black holes may not even exist.
There is really no reason to imagine that significantly charged black holes should exist, but figuring out if they do or not presents multiple conflicting issues. On one hand, we know of no process where net electromagnetic charge is not conserved. On the other hand, it shouldn't be possible for electromagnetic forces to escape from a black hole formulated in a classical manner. Experimentally, it would also be hard to distinguish charged matter in close orbit around a black hole from charged matter within the event horizon of the black hole itself, something that would have to be done with telescopes from many light years away for the foreseeable future.
In theory, the gravitational effects of matter and the gravitational effects of anti-matter are
indistinguishable and they can have angular momentum in the same way.
The
equivalence principle predicts that the gravitational acceleration of antimatter is the same as that of ordinary matter. A matter-antimatter gravitational repulsion is thus excluded from this point of view. Furthermore,
photons, which are their own antiparticles in the framework of the Standard Model, have in a large number of astronomical tests (
gravitational redshift and
gravitational lensing, for example) been observed to interact with the gravitational field of ordinary matter exactly as predicted by the
general theory of relativity. This is a feature that has to be explained by any theory predicting that matter and antimatter repel.
None of the direct experimental tests of this attempted to date have revealed anything to the contrary, and suggest that this is true, but experimental test are so far
inconclusive. This is because direct experimental tests are tricky to extract experimental results from because (1) most anti-matter lives for only fractions of a second in our matter dominated world (except in the case of anti-neutrinos), (2) the anti-matter we have to study involve particles no bigger than individual atoms which makes for a small target to observe and also means that the strength of gravitational forces relative to other forces at play is tiny, and (3) the propagation of individual particles needs to be understood using quantum mechanics and classical mechanics are only statistical averages of probabilistic quantum mechanical motion which is much more complex to analyze.
Purely Matter or Antimatter Sourced Black Holes Would Be Unphysical.
Because of the huge flux of neutrinos and antineutrinos through open space over a sufficiently long time, and the flux of photons, we can be confident that there is no such thing as a black hole formed purely from matter or purely from antimatter that can exist long enough to collide into another black hole.
Also, since there is no reason to believe that there have ever been antimatter dominated areas of the universe at any time more than a few moments after the Big Bang, the hypothetical proposed is not a physical possibility. This is because there can not physically be any black hole in our universe formed predominantly from antimatter.
The Internal Composition Of A Black Hole Doesn't Matter
But, honestly, the matter or antimatter or neither matter or antimatter status of the mass-energy that went into making a black hole is irrelevant anyway. A black hole doesn't have to have any matter inside it to gravitate in the same way. A black hole could be made up of pure photons within the event horizon, and the gravitational effect would be the same, and we would never know it because photons can't escape the event horizon any more than matter can, by definition. The inability of photons to escape is what makes a black hole a black hole.
It is possible as a result of Hawking radiation, which is strongly believed to exist in theory but has never been observed (because it is a tiny magnitude effect), but that doesn't change the fact that we don't know and can't really know what is inside a black hole. (There is a huge theoretical discussion regarding the "black hole information paradox" but for purposes of knowing the matter-antimatter-neither composition of what is within a black hole in any meaningful macroscopic way, it doesn't really matter.)
I would have to imagine that it retains its matter-like properties since it is indeed acting like matter in that it has mass. So I would also assume that the antimatter would also retain its antimatter-like properties.
None of those assumption are safe outside the domain of applicability of the laws of physics upon which they are based, which is in regions outside black holes. but, even if it did, as noted above, it wouldn't matter. Black holes made entirely of matter, entirely of antimatter, or entirely of photons, for example, would be indistinguishable from each other and behave identically.