A better question might be what is matter. Matter has mass, anything without mass is not matter.
electro magnetic radiation is not matter. The waves lengths contain energy, but not mass, and therefore electro magnetic radiation is not matter.
Particle accelerators can be used to accelerate particles that have mass and are matter to the point that the matter becomes energy.
The energy then can be seen to reappear as matter.
Energy can be turned into matter ( mass) and matter (mass) can be changed into energy.
The modern string theory proposes that matter itself is made of vibrations of a set mathematical formula. This implies that matter itself is vibrations not solid mass. In other words matter does not really exist, only vibrations.