Let ${\left[{\mathrm{A}}_{\mathrm{k}}\right]}_{\mathrm{n}\times \mathrm{n}}$be a square matrix of order n x n, such that${\mathrm{a}}_{\mathrm{ij}}=\left\{\begin{array}{c}0,\mathrm{i}\ne \mathrm{j}\\ \frac{1}{\mathrm{k}+\mathrm{i}},\mathrm{i}=\mathrm{j}\end{array}\text{ and }{\left[{\mathrm{B}}_{\mathrm{k}}\right]}_{\mathrm{n}\times \mathrm{n}}\right.$is its inverse
matrix, then which is/are true?