Uniqueness of row echelon form (Q1407477)

It is known that any matrix is row-equivalent to a matrix in row echelon form. However, while linear algebra or matrix theory textbooks often assert the uniqueness of the row echelon form of a matrix, relatively few actually provide a proof. The paper gives a new proof of the uniqueness of the row echelon form of a matrix. The present approach is based on more holistic properties of matrix products, the key ingredient being the notion of Hermite normal form.