i am having two problems here. The first one i am somewhat confident of:

1. Show that in general, for any square matrix satisfying:

then

i proceeded as follows:

while what i did seems legitimate...how do i show that the matrices must be square?

mr f says: Does a non-square matrix have an inverse ....?
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.