Eye question

We have (at least some of us, I guess) seen at some time, a diagram of the human eye focusing an image on the retina.  The image appears upside-down.   This is not a problem because the brain simply interprets the top of the eyeball as represening "down", the same direction as the feet, and the pull of gravity.

The brain's ability to "correct" or interpret this image has been demonstrated by getting people to wear prismatic glasses that invert the image back to "the right way up" on the retina.  People took a couple of weeks, but adjusted to it.

Now the human eyeball is basically a sphere, give or take a bulge at the lens, and the junction with the optic nerve.  It is rotationally symmetric about a line drawn from the centre of the lens to the opposite point on the back of the eye.  So images on the retina are inverted left to right as well.   Now there is no asymmetry to left/right like there is for up/down, so does the brain also correct for left/right reflection?  If it didn't for some of us, how would we know?  And would it matter?  How about left-handed people?   Am I missing something obvious here?