Hadamard invertible matrices, \(n\)-scalar products, and determinants (Q2387863)

Let \(A=(a_{ij})\) and \(B=(b_{ij})\) be two \(n\times n\) matrices defined over a field \(K.\) The Hadamard product of \(A\) and \(B\) is a matrix whose \((i,j)\) entry is \(a_{ij}b_{ij}.\) Therefore the Hadamard inverse of \(\,A=(a_{ij})\) is defined to be \(A^{-1}=(a_{ij}^{-1}).\;\)The main objective of the paper under review is to obtain relations involving \thinspace \(\det (A^{-1}).\)