I was thinking if I ha a image with a transparent background, is there a way to have that image appear like a square with a white background, but when the mouse hovers over it, only its background seems to change. like
You could wrap your image with a shrink-to-ft type wrapper and set the background on that intermediate element. That way #Library isn’t affected, but the background will change, and thus the transparent will.
Yes you can, if I understand what you want correctly: If the image with a foreground square/circle is made with a transparent background. Then you can apply a white/black background to it and change that on hover.
If you only want to cover the images on hover as I think was the other part of your question;
As your example images seems to be content in the html, a good way would be to wrap them in spans and use absolute positioned overlays with or w/o background color-image that will cover each image on hover. E.g.: