A Matrix that exchanges 2 or more rows is called a permutation matrix
Suppose we have a $3 \times 3$ matrix $A$ and we want to permute it's rows
Let's list all possible permutation matrices for $3 \times 3$
1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ \end{bmatrix}$ - permutes nothing
0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1 \end{bmatrix}$ - permutes 1st and 2nd rows
0 & 0 & 1\\ 0 & 1 & 0\\ 1 & 0 & 0\\ \end{bmatrix}$ - 1st and 3rd
1 & 0 & 0\\ 0 & 0 & 1\\ 0 & 1 & 0\\ \end{bmatrix}$ - 2nd and 3rd
0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0\\ \end{bmatrix}$ - 2nd, 3rd and 1st
0 & 0 & 1\\ 1 & 0 & 0\\ 0 & 1 & 0\\ \end{bmatrix}$ - 3, 1, 2
In how many ways we can permute rows of $I_n$?
$\begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix} \times \begin{bmatrix} a & b\\ c & d \end{bmatrix} = \begin{bmatrix} c & d\\ a & b \end{bmatrix}$
What if we want to exchange columns?
$\left[ \; \; \LARGE ? \; \; \; \right] \times \begin{bmatrix} a & b\\ c & d \end{bmatrix} = \begin{bmatrix} b & a\\ d & c \end{bmatrix}$
Can't put such a matrix on the left! Put in on the right instead
$\begin{bmatrix} a & b\\ c & d \end{bmatrix} \times \begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix} = \begin{bmatrix} b & a\\ d & c \end{bmatrix}$