OK here is the problem
im soo clueless =( any help would be awesome
Here's a start. Let C be a p x m matrix. Then CA is a (p x m)(m x n) = p x n matrix. But CA = In. Thus C is an n x m matrix. Do this again for AD. What does all this mean for A?
I fixed the problem. Unfortunately that makes my comment pointless.
The following facts may be useful:
Also, if is an matrix, it is true that
Furthermore, it is also true that
Using these facts, as well as facts about the minimum function, you should be able to prove both that and that thus proving your result.
Can you see your way forward?