Inequalities for permanents of hermitian matrices

For given integers n1, n2 ≥ 1, we consider two hermitian matrices of order n = n1 + n2, written in block form: , where every matrix Xij has dimension ni × nj, 1 ≤ i, j ≤ 2. It is proved that if A11 ≥ B11 ≥ 0, A22 ≥ B22 ≥ 0, then per A ≥ per B ≥ 0.