 Permutation matrix

A permutation matrix has exactly one entry equal to one in each row and column and zeros elsewhere. Left or right multiplication permutes coordinates, and $P^{-1}=P^T$.

A permutation matrix is a special type of square binary matrix that is used to represent a permutation of a finite set. Specifically, it is an \( n \times n \) matrix that contains exactly one entry of 1 in each row and each column, and all other entries are 0.