One natural model (see ) is a pair of matrices of decision variables. The expression for the determinant is cumbersome but, at orders 4 and greater, there is some repetition which can be assigned to a single variable.

Exchanging a pair of rows or a pair of columns of a matrix negates the sign of the determinant. Hence, this problem does not quite have row and column symmetry. However, if we insist that the absolute value of the determinant is 1 then we can apply row and column symmetry breaking, for example by lexicographic and all-permutation ordering. If a solution has a determinant of -1 (and we are solving a variant where a positive determinant is required) we can simply exchange a pair of rows/columns in the solution.

The problem also has diagonal symmetry which can easily be broken by adding further symmetry-breaking constraints (again, see ).

1. A. M. Frisch, C. Jefferson, I. Miguel, “Constraints for Breaking More Row and Column Symmetries,” Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming, 2003.