I'm not really sure how to answer this question. I can do pretty well at these simply by visualizing the rotation, and in a casual setting, where not much hinged on getting it right, I would probably just use that method because it's a lot faster and easier. But consciously checking relations does improve my performance (or at least feels more reliable), so if I was in a context where it was important to get the answers right, that's what I would do.

It's like asking whether I add up three-digit numbers in my head or work it out on paper. Depends on the context.