here is my problem and what I did:
If 0<a<b, prove that 0<a^2<b^2
0<a^2<ab and 0<ab<b^2
Or would doing something your way be better?
then, you are asked to prove: (we are not considering negative numbers here, of course)
thus, assume to the contrary that but
then in much the same way as you did the last problem, you can show that that would mean , but that is contrary to our assumption