If P1 is an even permutation matrix and P2 is odd, deduce from P1 +P2 = P1(P T 1 + P T 2

Step 1 of 4

A permutation matrix P has the same rows as the identity (in some order). There is a single “1” in every row and column. The most common permutation matrix is  (As it exchanges nothing). The product of two permutation matrices is another permutation – the rows of I get reordered twice.

An even permutation matrix is when we can represent the matrix as a product of even number of transpositions. Determinant of even permutation matrix will be 1.

An odd permutation matrix is when we can represent the matrix as a product of odd number of transpositions. Determinant of an odd permutation matrix will be -1.