This article discusses the permutation matrix, which is a weak commutation matrix. This weak commutation matrix is determined by compiling the duplicate entry, i.e., two, three, and four which are the same in different positions in the 4 × 4 secondary diagonal matrix. It uses the property of the transformation vec matrix to vec transpose the matrix for determining the weak commutation matrix of the secondary diagonal matrix. We have 24 weak commutation matrices for the secondary diagonal matrices.

Keywords : Keywords:-Weak Commutation Matrix; Duplicate Entries; Secondary Diagonal Entry; Vec Matrix