On cofactor expansion of determinants of Boolean matrices

We give necessary and sufficient conditions of a cofactor expansibility of determinants along a row or column for Boolean square matrices over an arbitrary Boolean algebra. First of all we define a natural decomposition of an arbitrary Boolean matrix by interior, exterior, and determinate parts. The introduced notions allow us to establish the main result of this paper. It is shown that the formulas of the cofactor expansion along a row (column) of determinants of an arbitrary square Boolean matrix hold if and only if the formulas of the cofactor expansion along the corresponding row (column) hold for determinants of its interior part.