  The commutation matrix was first introduced in statistics as a transposition
matrix by Murnaghan in 1938. In this paper, we first investigate the
commutation matrix which is employed to transform a matrix into its transpose.
We then extend the concept of the commutation matrix to commutation tensor and
use the commutation tensor to achieve the unification of the two formulae of
the linear preserver of the matrix rank, a classical result of Marcus in 1971.
