I'm making a plexiglass shelf door (2 actually). Dimensions are 3500x7500x3. And I don't know if I need a frame for that. I wanted to attach it with 2 [that thing that lets you open doors] and one magnet on the other side.
Plexiglas can be fairly flexible, unless you get thicker (more expensive) sheets. If you're happy with how it looks/feels, then you could mount it directly... but glass is more commonly used "bare" this way due to its greater rigidity.
I had a plexiglas desktop, about 5mm thick, the longest edge being around 75cm. Even at this thickness, it does bend. On the other hand, if you're making doors which are to be in an upright position, the balance point is completely different. You say that you're planning on attaching it with two hinges, and at length 75cm, thickness 3mm, it does sound risky to me. 3mm thick is simply very vulnerable so if any twisting pressure gets exerted to it due to balance point, it could start to crack from any which point where you drilled holes for attaching the hinges. I would either choose a far thicker plexi, or a little bit thicker one with more than 2 hinges, or just play safe by making a frame and attaching the hinges and handles into that. Plexiglas doesn't take twisting too well.