matrices, inverses, transposes, r.r.e.f...

Ok.. I have a series of problems..

I have a square matrix, P, I also have a function, F, that computes < m x n matrix|m x m identity matrix>

I have to find F(P), F(Transpose(P)), F(P . Transpose(P)), F(Transpose (P) . P)

I also have to find their row reduced echelon forms and comment on their results

obviously some of these matrices are square, and so the row reduced echelon form of F finds their inverse.. but what about for those that arent square?

what are the comments I should be making?

many thanks