Every time the light beam hits a mirror it isn't all reflected, some of it is absorbed, so the beam would light up a shit ton of the room before slowly dissipating lol
The problem with the question is that it is impossible to know the answer. Simply being present to see it would make a change to the room. And the addition of a light source to allow vision would do the same. So by observing, you have destroyed the purity you sought to observe.
The light would be absorbed after bouncing a bit. Every time it bounces, it would be absorbed and converted into heat until the light died and the mirrors were slightly warmer. Not sure if this is right, I am only 13; sorry if it's wrong.
But these mirrors are layered... they can reflect each other if there is a light source. The question was if the walls and floor and ceiling were made of mirrors, with no extra mirrors in between.
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