Prove that, if a is a Real Number and 0 < a< 1, then (a^2)<1

Could someone please help me with this, I also have to give reasoning for each step. Thanks.

Could you show us what you have already worked out, thought to work out, or your ideas on it first? If we know your thoughts on the matter, we can help guide them or improve upon them so that you can see the solution. We're not here to do your work for you. We're here to help you think!

what theorems can you use? have you previously shown that if b < c, and m > 0, that mb < mc?