On an open problem concerning regular magic squares of odd order

In this paper we give an answer to an open problem posed by M.Z. Lee et al. (2012) [2]. More precisely, we prove that the classical regular magic square of odd order produced by the centroskew S-circulant matrix with the assignment aj=j−1, j=1,2,⋯,(n+1)/2 is always nonsingular. Moreover an explicit formula for computing the eigenvalues of classical regular magic squares of odd order is given.