Remarks
-
Of course the identity has sign 1, because it can be written as
the product of zero transpositions. If you dislike such a
product of zero elements, then write e = (1,2)(1,2),
the product of two transpositions (for Sn
with n at least 2).
-
We will shortly
discuss
a practical way of determining the sign.
-
Permutations and the sign of permutations are the ingredients
in the definition of the determinant of a square matrix.
Once we know more about the sign, the definition
of the determinant is discussed further.