A formula for the determinant of a square matrix I saw the following formula for the determinant of an $n \times n$ square matrix $A$:
$$\det(A) = \sum (\pm) a_{1j_1}a_{2j_2}\cdots a_{nj_n}.$$
The sum being taken over all permutations of the second subscripts. The algebraic sign preceding each term is determined by the arrangement of the second subscripts. The formula is taken from Matrices and Linear transformations, 2nd edition, by Charles G. Cullen. 
My question is, in the above formula, what is the purpose of the pair of parentheses that enclosed the symbol $\pm$? The same formula is also found in other texts, for example Elementary Linear algebra with Applications, 9th edition, by Bernard Kolman and David R. Hill.

The same formula without the parentheses can also be found in places.  So it's not  necessary.  All it means is $sgn(\sigma)$.  
