I am confused about one property of determinants which is: interchanging two rows or columns of a determinant changes the sign of the determinant. Does it mean that when I interchange rows of a determinant several times the sign keeps changing or it changes just once?
Example
$$\det A = \begin{vmatrix} 2 & -1 & 1 & -1\\ 3 & 3 & 0 & 2\\ 1 & 2 & -1 & 1\\ 2 & 5 & 1 & 2 \end{vmatrix} = - \begin{vmatrix} 1 & 2 & -1 & 1\\ 3 & 3 & 0 & 2\\ 2 & -1 & 1 & -1\\ 2 & 5 & 1 & 2 \end{vmatrix} = - \begin{vmatrix} 1 & 2 & -1 & 1\\ 0 & -3 & 3 & -1\\ 0 & -5 & 3 & -3\\ 0 & 1 & 3 & 0 \end{vmatrix}$$
where, firstly, the 1st and 3rd row were swapped, changing sign of determinant, and then the 2nd and 4th rows were swapped (changing the sign of determinant or not?).
The sign changes every time you switch rows.