Space is not matter in the sense that it is not composed of particles. Tendencies are to describe space in terms of plasma. This because plasma too will propagate electromagnetic fields and carry electric charges. This view though closer to the truth than the concept of empty space is still not completely accurate. A plasma is made up of particles.
Space exists between particles.
When you look at a solid object it is really not solid at all. There is more space contained in solid matter than matter itself. Each tiny particle is separated from all other particles by space. Similar to the separation between the stars and planets. When looking at the universe as a whole, there is more space than actual matter.