Answer :
Examples of permutation matrices are the identity matrices with a permutation in rows. Permutation matrices are invertible and the inverse is a permutation matrix as well.
A permutation matrix is a square matrix which contains exactly one 1 in each row and all other entries 0.
So a permutation matrix can be obtained by rearranging the rows or columns of an identity matrix. Identity matrix is also a permutation matrix with entry 1 exactly once in each row and all other entries 0.
Example of a permutation matrix:
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]
A permutation matrix is invertible because an identity matrix is invertible [since det(I) = 1] and a permutation matrix is just got by exchanging rows or columns which does not change its determinant. So the determinant of a permutation matrix ≠ 0 and hence invertible.
The inverse of a permutation matrix is its transpose itself. The transpose is again a permutation matrix.
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