Since black holes have a mass and a size, one can define
a density. This means a black hole consists of matter. Does science define the matter of a black hole ?
The “matter” of a black hole is the quantum singularity, a single particle of infinite density, consisting of all the matter the hole absorbed.
No better explanation of black hole mass exists pretty much because neither quantum mechanics nor relativity can explain the goings on in the immediate vicinity of a singularity.
Also, the socalled “size” of a black hole is usually defined to be that of the event horizon* surrounding the black hole. As enolancooper alluded to, the actual physical size of the hole itself is that of a point.
[sub]*The “event horizon” is the boundary surrounding a black hole within which the escape velocity of the hole exceeds c. Once you go in past that, you don’t come out.[/sub]
There is a theorem known as the nohair theorem. A black hole has no hair. It states that the only properties of a black hole are mass, angular momentum, electric charge, and (if magnetic monopoles exist) magnetic charge. The size and shape of the event horizon depend on these properties. All other properties are lost. You cannot distinguish between a black hole made of matter from one made of antimatter or even from a black hole made of enough energy.
If you have a black hole of mass M, and divide the volume contained within the event horizon by the mass, you will get the critical density D[sub]M[/sub] for a mass of M. Any time you have a mass of M in a sphere with a density of D[sub]M[/sub], it will collapse into a point and from a black hole.
Black holes are formed from the collapsed cores of “dead” large stars.* So, they formed from matter (i.e., you don’t need to realize there is density before you realize there is matter).
As has been said, all matter that formed/enters a black hole is squished into the singularity…a point with mass and essentially infinite density.
The singularity itself is something that modern physics cannot describe, so I’m not so sure if “science can define the matter of a black hole” once it’s part of the singularity.
Including the event horizon in the density calculation is inappropriate because the event horizon is not a physical thing…it’s just a distance from the singularity.

 unless we’re talking about primordial black holes that are believed to have formed at the beginning of the universe.
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Can someone explain to me how a black hole can have an EM charge to an outside observer? Wouldn’t this mean that information is leaving the event horizon?
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I can try, but this IS from the perspective of a nonexpert…
In order to observe a black hole, one thing you could do is find a candidate by some way or another, drop off a little test mass, and see what happens. You do enough math and you find out what effect a black hole would have on how things move under the absence of external forces.
Now suppose the black hole is one that has electrical charge. When you work through the same math, the fact that it has electrical charge means that your little test mass will move differently. Thus, one way of telling if a black hole is charged or not would be to see what effect it has on the paths of objects like asteroids, spaceships, people, etc.
On a more prosaic level, if it has electrical charge, it has an electric field. That means that a little charged mass would move differently from an electrically neutral mass.
As for information leaving the event horizon, well… Really, for a regular black hole, no matter or energy (hence including light) can get past the event horizon, but that doesn’t mean we can’t tell how massive the black hole is. The size of the event horizon itself tells us that much, so it’s obviously possible to infer a few basic things about the black hole (as was stated, its mass, charge, angular momentum, and “magnetic” charge, if such a thing exists, as well as something we think of as temperature).
Actually, I seem to recall that the nature of the horizon is different for the charged black hole (I think it has two, and you could conceivably get past one but not the other, but I’d have to check on that).