Yes, you can purchase a magnifying mirror and either use a suction cup or glue it to the inside of the cabinet provided there is interior clearance. However, I find I usually need to be able to get very close and move and angle the mirror to be able to see clearly.

Your other option is to purchase one on a swing arm and mount it on the wall. I think it's helpful to have a mirror that provides additional light to see things easier.

This one is battery operated so it doesn't need to be plugged in.

There was a swing arm mirror similar to that one (not lighted) in this house when we bought it two years ago. I love that thing! Don't know what I did before I had it! I am going to have it reinstalled after the remodel is done. Yes, I'm of a certain age, too. :)