A square matrix is called a permutation matrix if it contain

A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the permutation matrix A = [0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0].

Solution

The transpose of a permutation matrix is its inverse. Thus, for the given matrix its transpose it its inverse. Transpose of a matrix can be given by interchanging its rows by its columns.
Thus A^-1 = A^T =
[ 0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0 ]