Magic “Squares” Indeed!

6392 + 1742 + 8522 = 9362 + 4712 + 2582 (counter-diagonals) 6542 + 7982 + 2132 = 4562 + 8972 + 3122 (diagonals) 6932 + 7142 + 2582 = 3962 + 4172 + 8522 (counter-diagonals). This property was discovered by Dr. Irving Joshua Matrix [3], first published in [5] and more recently in [1]. We prove that this property holds for every 3-by-3 magic square, where the rows, columns, diagonals, and counter-diagonals can be read as 3-digit numbers in any base. We also describe n-by-n matrices that satisfy this condition, among them all circulant matrices and all symmetrical magic squares. For example, the 5-by-5 magic square in (1) also satisfies the squarepalindromic property for every base.