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It is weird that I have a camera that has a left-handed coordinate system.
All the other cameras are right handed.
Left handed camera:
Right handed camera (all others are right handed, too):
I can't tell what caused this.
As hinted at by cegaton, you set the x-dimension of the scale to a negative value for one of the cameras. Open the properties region with N and set the scale back to positive 1 if you like.