Elementary row operations on a matrix preserve row space, null space, rank, nullity, and invertibilty. They do not preserve determinant, trace, or column space.
Inspired by List of matrix properties which are preserved after a change of basis , I would like to ask:
Are there any other interesting properties preserved by elementary row operations?
Best Answer
One of the most important: If a matrix is viewed as an augmented matrix consisting of a coefficient matrix and a RHS vector, then the solution set is invariant under row operations.