A square matrix is a matrix for which horizontal and vertical dimensions are the same (i.e., an 
matrix).
A matrix 
may be tested to determine if it is square in Wolfram
Language using SquareMatrixQ[m].
Let 
be a positive
integer. Consider the numbers of 
matrices containing each
of 
distinct symbols exactly once. The
number of distinct matrices modulo rotations and reflections for 
, 2, ... are given by 1, 3, 45360, ... (OEIS A086829).
Consider an 
matrix consisting of the integers
1 to 
arranged in any order. Then the maximal determinants
possible for 
,
2, ... are 1, 10, 412, 40800, 6839492, ... (OEIS A085000).
Consider an 
matrix with single copies of the integers
1, 2, ..., 
and the rest of the elements zero. Then the triangle of 
matrices with 
, 1, ..., 
distinct nonzero entries that are rotationally and reflectively
distinct is 1, 1; 1, 1, 2, 3, 3; 1, 3, 12, 66, 378, 1890, 7560, 22680, 45360, 45360;
... (OEIS A087074).
