A matrix for which horizontal and vertical dimensions are the same (i.e., an n×n matrix). A matrix m may be tested to determine if it is square in Wolfram Language using SquareMatrixQ[m]. Consider the numbers of n×n matrices on n^2 distinct symbols. The number of distinct matrices modulo rotations and reflections for n = 1, 2, ... are given by 1, 3, 45360, ... (OEIS A086829). Consider an n×n matrix consisting of the integers 1 to n^2 arranged in any order. Then the maximal determinants possible for n = 1, 2, ... are 1, 10, 412, 40800, 6839492, ... (OEIS A085000).
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