Necessary and sufficient on the computation of determinant of a kind of special matrix

One of the specific matrices having special characteristics and applications is centrosymmetric matrix. Recently, the algorithm of determinant this matrix by applying the algorithm of lower Hessenberg's determinant was computed. Detection of the determinant in the beginning process is needed on those areas, therefore in this paper, the necessary and sufficient of the algorithm is presented. Some numerical examples of determinant of centrosymmetric matrix are given for deeper understanding.