Yes, some are straightforward. Most are not. For example, suppose a student shows that T: V --> W is bijective and linear on the way to proving a solution to an

Yes, some are straightforward. Most are not. For example, suppose a student shows that T: V --> W is bijective and linear on the way to proving a solution to an exercise. The textbook solution shows dim(V) = dim(W) and T is injective instead. Another student shows that dim(V) = dim(W) and T is surjective, and still another student simply uses the rank-nullity theorem directly All of these solutions are equivalent (or at least, may be if there are no other mistakes). There are probably other equivalent formulations that I can't immediately think of. But each of these students may see the solution and not realize that they're equivalent. Or worse, they may understand the equivalence of the foregoing statements but make a critical flaw elsewhere in the proof, and still think they have the correct solution. I'm not arguing against solutions in textbooks. I'm just saying that for most proof-based mathematics they wouldn't be useful as solution checkers.