Writing step-by-step solutions to homework exercises and retaining a hard copy of all work submitted is critical because it allows you to see how a problem is solved, rather than just the answer. Keeping a copy allows you to study from it and also serves as a backup in case one copy gets lost.
Work Step by Step
Writing out your work step-by-step helps you to understand how you get a solution, as well as where you might have made a mistake. Keeping a copy is just good practice, because you can refer to it later. Instructors lose things too, and having a copy will help you review for future classes as well. Plus, it is a nice boost to be able to look back and see how much you got done!