For specific, perplexing problems, Math Stack Exchange (MSE) is invaluable. Search "MSE dummit and foote 10.3 exercise 12" to find peer-reviewed, upvoted responses. The community is strict about correctness.
I’ve already checked the usual places (official solutions don’t exist beyond selected exercises, and most online solution sets stop at Chapter 9 or cover only Chapters 1–7). dummit and foote solutions chapter 10