I am having two problems here. The first one I am somewhat confident of:
1. Show that in general, for any square matrix satisfying:
I proceeded as follows:
While what I did seems legitimate...how do I show that the matrices must be square?
2. Let A, D, and P be n X n matrices satisfying . Solve for A. Must it be true that A = D?
For this one I am not sure how to proceed. In order to get rid of P I need to say multiply by but that doesn't seem to help me... Same sort of situation for P.