There is a quantity called escape velocity:
v e s = sqr(2GM/R)

where M is the mass of the central body, G is the gravitational constant (6.67×10⁻¹¹ m³·kg⁻¹·s⁻², R is its radius (assume it spherical).

So normally we would use this to compute the escape velocity of a projectile. For example, if a projectile launched from Earth exceeds 11.2 km/s, then that projectile has sufficient energy to leave the gravitational influence in the sense of a bound orbit from Earth -this orbit would be hyperbolic- once it leaves Earth it never comes back and at VERY large distance from Earth it has a non-zero velocity With Reference To (WRT) Earth. Escape velocity from the Sun at Earth distance is about 42 km/s if I recall.

Now WRT black holes, if we have their mass and radius then we can calculate escape velocity. So if we DO THAT and find that escape velocity EXCEEDS c, speed of light, you have the answer. A light ray emitted from the “surface” of a black hole would orbit the black hole and not escape.

So, this explanation is NEWTONIAN and does not involve relativity. But the answer you get is the same: a beam of photons traveling at the speed of light has insufficient energy to escape a black hole.

Yes exactly, light is also a matter which interacts with gravity in a similar way as other matters.

Einstein's gravity theory (general relativity) interprets gravity as curved space-time, which affects anything that travels in space-time. But light itself also induces interaction (like Coulomb interaction) between matters that carry electric charges.

Gravity is the warping of space and time caused by the presence of mass (or energy). This means that gravity affects anything that exists in space, which includes matter but also energy, such as light.

An analogy that I learned is that space moves, almost like it has currents, toward mass, and this movement is what we experience as the force of gravity. At the event horizon of a black hole, the speed at which space is falling inward toward the hole is the speed of light. Outside the event horizon, space is flowing slower than light. Inside of the event horizon, it is flowing faster than light. Because light has a finite speed and nothing in space can travel faster than light, anything that passes through the event horizon will continue to fall in, no matter how fast it is moving relative to the space around it. This analogy isn't perfect, but it gives an illustration of why even light can be trapped by a black hole.

Light is both a wave and a particle, isn't it? And the particle properties of light might give it gravity.

1. NASA is certainly a reliable site and Scientific American should be too:
No light of any kind, including X-rays, can escape from inside the event horizon of a black hole, the region beyond which there is no return. ... The immense gravity of black holes also distorts space itself, so it is possible to see the influence of an invisible gravitational pull on stars and other objects.