Is the determinant of a matrix preserved under permutations of the rows/columns of the matrix?
If not, is its absolute value preserved?
[Math] Is the determinant of a matrix preserved under permutations of the rows/columns of a matrix
linear algebramatrices
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Best Answer
Any single exchange of two rows or two column changes the sign of the determinant. You need to keep track of whether you do an odd or even number of switches of rows or columns. That is to say, you need to multiply the determinant by $\mathbb{sgn}(\sigma)$, the sign of the permutation $\sigma$ for any given row or column permutation.