Their is a broad consensus among physicists that matter will be gravitationally attracted to antimatter. Unfortunately, it is very hard to test this because antimatter is so rare, and annihilates with matter. Also, because the only way to create antimatter is to have high energy particles, which doesn't provide a great environment for studying gravity's effects. Fortunately, just this year, ALPHA, at CERN, trapped antimatter atoms and used them to free-fall with matter. Time will tell soon what the answer is.
Many arguments support the idea that the two attract. The idea of "antigravity" (where the two types of atoms repel instead of attract) seems to violate the conservation of energy principle and is a CP violation. Also, using E=MC^2, because of the energy-matter equivalence, the two types of atoms should attract. Also, the photon is its own antiparticle, and is attracted to matter, so it should likewise be attracted to antimatter.
However, antigravity would solve several major problems in physics. One, it would clear up the problem of baryon asymmetry after the big bang, as matter and antimatter repeled, galaxies of matter in one place, galaxies of antimatter in another, continuing to move apart. Two, it explains partially why the expansion of the universe is accelerating; if gravity were always attractive, it should be decelerating. Finally, it is an alternative to the theory of "dark matter", and explains the problem of galaxy rotational speeds. However, many scientists have come up with explanations for this that leave out the idea of antigravity, by pointing out potential contradictions in the first and second problems, and "dark matter" itself, which has been postulated time and time again and appears in most general equations in the final one.
Antigravity can be shown to be a prediction of the General Theory of Relativity, but universal attractive gravity (where matter and antimatter attract) can be also. CPT-transformations resulting in CPT symmetry produce the idea of universal attractive gravity, but CPT asymmetury produces the idea of antigravity. This is a hard problem, and one that will hopefully be resolved soon in the particle chambers. It will most likely result in the theory of universal attractive gravity, but who knows, we may be surprised to learn of antigravity - and if its existance is true, this will totally rethink our visualization of the universe, and will solve a lot of problems that we don't have a definite answer to.
The CERN ALFA2 experiment will confirm what is obvious to those willing to see at larger scales.
1. The Blue spikes above thunder storms have been shown to contain antimatter and travel in the opposite direction from their local matter gravity. (Fermi gamma-ray space telescope) or (The Riddle of Antimatter) at youtu.Be/Y5oNwJNdMxY)
2. The jets from the center of the galaxy (Black hole) contain antimatter and travel in the opposite direction from their local matter gravity. (Fermi gamma-ray space telescope) The only thing that can leave a black hole is gravity repelling antimatter.
3. All of the fallowing would not be needed:
a. Big bang, matter and antimatter would be created from energy in all of space.
B. Inflation, not needed see above.
C. Dark matter, a large cloud of gas would form around each galaxy.
D. Dark energy, galaxies would be attracted to like matter galaxies and be repelled by opposite matter galaxies.
4. The amount of antimatter in the universe would be equal to the amount of matter.