Singular matrices applied to 3 × 3 magic squares

Abstract

If you enjoy magic squares and their unusual and fascinating numerical properties, you are in good company. Indeed, many a professional mathematician, scientist and amateur has shared the same interest. Technical research work on the properties of magic squares is available aplenty in the literature or in books concerned with the recreational aspects of mathematics. Studies of magic squares naturally lead to some elements of group theory, of lattices, of Latin squares, of partitions, of matrices, of determinants, and so on …By definition, the general n x n magic square is a square array of n2 numbers {aij; i, j = 1,2,... , n) whose n rows, n columns, and two main diagonals have the same sum s. It is therefore natural to think of a magic square as a matrix and we shall do this in the present note, simply referring to it as a magic matrix.