Question

Is light a matter?

Answer 1

Everything, including light, in quantum mechanics is both a particle and a wave (really, it is a definite something that has both wave-like and particle-like properties). So if you think matter is something that is made of particles, either everything is or isn't matter depending on how you look at it.
In fact, I think that is the wrong way to think about it. What you really want to know is: does light have properties that other kinds of particles don't? The answer is yes. Most of the particles that make up everything we traditionally call matter are called "fermions".