In this paper, we consider in the product of Banach spaces X₁ X₂ Xₙ, the n × n-block matrices of linear relations in the form, M: = pmatrix A₁, ₁ A₁, ₍ \\ \\ A₍, ₁ A₍, ₍pmatrix, , where the entries of the matrix are in general unbounded linear relations and satisfy the following conditions: A₈, ₉: Xⱼ Xᵢ, i, j \1, , n\. . Studying the spectral properties of M, it is natural to take stability of closedness for this matrix. So, we have to study this problem in the present paper. In addition, we show under some suitable conditions that M is a Fredholm linear relation.
Ammar et al. (Wed,) studied this question.