No, light reflecting in a massless cavity would not possess the qualities of mass. Light, or photons, are particles that have zero rest mass. Massless particles travel at the speed of light in a vacuum and do not experience gravitational forces. They have energy and momentum but not mass in the traditional sense.
When light reflects off a surface, such as in a massless cavity, it experiences a change in momentum due to the transfer of momentum to the surface. However, this momentum change does not imply that the light itself has acquired mass.
Mass is a property associated with particles that have rest mass, such as electrons or protons. These particles have inertia and are subject to gravitational forces. Light, on the other hand, is composed of massless particles, and its behavior is better described by its energy, wavelength, frequency, and momentum rather than mass.
So, while light can carry energy, momentum, and other properties, it does not possess mass, even when reflecting in a massless cavity.