Inverting an image, as a matrix
I tried it on square grayscale images myself (just hoping they would be invertible, which was always the case (not much luck involved here, since invertible matrices lie dense)). I added a few examples so you can judge the inverses yourself. Their precise look of course depends on the particular normalization (I used cv2.normalize and also normalized manually by

as done here (I used this to create the LaTeX expression)).



Moreover, I ran this procedure on all test/cat images from CIFAR-10. You can find the results here. Notice that actually a lot of these 32x32 images were (as a matrix) not invertible.
As was asked for by user fiveclubs, here are the normalized inverses of the normalized inverses. They are nowhere near their originals.
Dolphin inverse of inverse:

Painting inverse of inverse:

Tower inverse of inverse: