Bathroom Cabinet Question

I looked at a bathroom medicine cabinet at Home Depot. It is not recessed in the wall. It had hinges on the left (facing the mirror). Is it possible to turn it upside down so the hinges are on the right and it opens out different? Would it look like somebody goofed?
Second question. Reason for this... the vanity is sitting in a corner. The wall to the left houses a built-in, small medicine cabinet. It is covered in formica and has no mirror. The mirror - just mirror, no cabinet - sits over vanity. Question: In order to make the larger cabinet with mirror work, I have to hang it so it is flush with right side of vanity instead of centered in the middle the way mirror is now. Will that look like further goof? This is small bath and I need as much storage space as possible.
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it should look identical if the face was symetrical. check to see if the shelves will stay in, or the supports can be turned over, when you turn it upside down though.

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