A mirror couldn't be white, as then you wouldn't be able to see your reflection so clearly. It wouldn't be transparent, as that then won't reflect.
So what color is it?
A mirror, or a perfect mirror at least, is the same colour as a perfectly white sheet of paper.
Both a perfect mirror and a perfectly white sheet of paper reflect all the light that hits them. The difference is that the paper scatters the light so what reaches your eye is a mixture of all the light hitting the paper, while the mirror reflects the light without scattering. If you're interested in details the reflection from a mirror is specular while the reflection from the piece of paper is diffuse.
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The eye contains three types of cone cells that detect red, green and blue light. Your brain works out the colour based on how much the three types of cells are activated e.g. if only the red cones report a signal the brain interprets this as red light. If all three types of cone are equally activated the brain interprets this as white light.
A sheet of paper scrambles the light hitting it so if you try to use the paper as a mirror all the light hitting it gets mixed up and all types of cone cell receive light from all bits of the paper. Assuming you're not standing in a red painted room or somewhere there's an obvious colour cast the paper will look white.
If you swap the sheet of paper for a mirror the light isn't scrambled. If you're looking at e.g. a beachball some of the cone cells in your eye will receive light from the red bits of the beachball, some from the yellow sand, some from the blue sky and so on. So the individual cone cells are seeing the colour of the scene you're reflecting in the mirror not the colour of the mirror itself. In this sense the mirror doesn't have a colour. However if you average over all the cone cells, i.e. mix all the light up, you'll get the same colour as when you had the sheet of paper there. That's why I claim the mirror has the same colour as the piece of paper.
Of course you could argue the paper doen't really have a colour either. After all the paper may look white in daylight, but it would look green in a jungle or red in a tomato sauce factory.
There is a nice vsauce episode on exactly this subject. There they argue that for all intents and purposes, a mirror is a non-diffuse type of white surface (a "smart" kind of white).
However, when measuring more carefully, a mirror is actually slightly green. Most common mirrors reflect light from the green part of the spectrum better than from other parts, making the mirror's true colour greenish. This is only noticeable when placing two mirrors opposite each other, and looking into the mirror-tunnel thus created -- far off "in the distance", your face looks distinctly greener than your face close by.
Vsauce answered this question exactly in one episode. I suggest checking it out, it explains the different ways the eyes see the mirror, and gets right to the point.
I guess this would be more of philosophical question rather than scientific. Mirror would take color of any object being reflected on it so it would have variable color. If you remove the reflectivity from the mirror to see the color of the material, then it is not a mirror anymore.
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