Colour Vision ?

Have you ever thought about our eye sight?  When I was at school, perhaps I was around fourteen, I watched an episode of a television series, "Tales of the Unexpected.."  The gist of the tale was that a woman who couldn't see had her vision restored by a double eye transplant.  The catch to the tale was that the eyes which were transplanted belonged to the wife of the recipients lover whom he had murdered.  But its not the catch that's important, its the thoughts and conclusions that the tale started.  And as yet, thirty six years later, I still aren't able to find a way to prove my conclusions.
On my way to school on the bus the next morning I was thinking about the programme and wondering what it would be like to see the world through someone else's eyes.  My initial thought was that it would be just as I see the world, as everyone sees the world surely it must.  But then I had another thought would things look the same through another's eyes for instance does everyone see the colours the same? Could the colour I see as green be, when seen by someone else, be the colour I would think of as red.  After all colour could be all our brains interpretation of what the eyes see and the brain is so complicated that I'm expect everyone has a completely different thought pattern.  So if I could see the world through another persons eyes it could might look completely alien.  Just imagine what the world would look like with all the colours mixed up.  But surely this can't be or can it?  I would say yes it is possible and I can think of no way to prove that we all see colours the same.  In fact I think it very likely that  we all see the world differently.  Can anyone correct me and explain how to prove I'm wrong?  If so please let me know