A permutation matrix, denoted as P, is a square matrix that represents a permutation of the rows or columns of an identity matrix.
When you multiply a permutation matrix on the left side of a matrix A (PA), it actually permutes the rows of matrix A according to the permutation represented by the permutation matrix P.
PA = A (with row of A swapped acc to permutation of P)
Similarly, when you multiply a permutation matrix on the right side of a matrix A (AP), it permutes the columns of matrix A according to the same permutation represented by the permutation matrix P.
AP = A (with columns of A swapped acc to permutation of P)
Here, $AI_{12}$ hence multiplying permutation matrix on right side of A and 1st row and 2nd rows of P are exchanged (exchanging 1st 2nd rows or exchanging 1st 2nd column of $I_{12}$ is equivalent).
Hence $AI_{12}$ will record exchanging 1st and 2nd columns of matrix A.