Matrices with prescribed characteristic polynomial and several prescribed submatrices

Let A = [Ajk ],j,k = 1,2 be a partitioned matrix. We consider the problems: find necessary and sufficient conditions for the existence of A if we prescribe (i) An and the characteristic polynomial ofA, or (ii)A 11,A 22, and the characteristic polynomial of A. We solve (i) and give a partial solution of (ii).