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(b) The number of inversions is .
(c) There are zero inversions in this permutation.
DEFINITION
A permutation is called even if the total number of inversions is an even integer and is called odd if the total number of
inversions is an odd integer.
EXAMPLE 4 Classifying Permutations
The following table classifies the various permutations of {1, 2, 3} as even or odd.
Permutation Number of Inversions Classification
(1, 2, 3) 0 even
(1, 3, 2) 1 odd
(2, 1, 3) 1 odd
(2, 3, 1) 2 even
(3, 1, 2) 2 even
(3, 2, 1) 3 odd
Combinatorial Definition of the Determinant
By an elementary product from an matrix A we shall mean any product of entries from , no two of which come from the
same row or the same column.
EXAMPLE 5 Elementary Products
List all elementary products from the matrices
(a)
