Veritasium talked about this in one video. If you are in a room or a train, plane, car or whatever just a closed space traveling at the speed of light and you put a mirror in front of you, could you see your reflection? I think the answer is no because light can't travel 2 times "c", light can't travel from you (because you already go to that speed) to the mirror.
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1If you don't want your question closed quickly as a duplicate, you must modify your question since, as has been asked and answered here too many times to count, there is no inertial reference frame with speed $c$. – Alfred Centauri Apr 02 '15 at 00:43
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possible duplicate of reflection at speed of light when both mirror and viewer is travelling at the speed of light – Alfred Centauri Apr 02 '15 at 00:44
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possible duplicate of Can you see yourself in a mirror when you are riding on top of a light stream? – ACuriousMind Apr 02 '15 at 01:20
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See also my answer here – Kyle Kanos Apr 02 '15 at 02:59