Magic "Squares" Indeed!

A real matrix is called square-palindromic if, for every base \(b\), the sum of the squares of its rows, columns, and four sets of diagonals (as described in the article) are unchanged when the numbers are read "backwards" in base \(b\).  The authors prove that all \(3 \times 3\) magic squares are square-palindromic.  They also give sufficient conditions for  \(n \times n\) magic squares to be square-palindromic, which include all circulant matrices and all symmetrical magic squares.