Let's say I have a matrix A of arbitrary size, and I perform a finite number of both elementary row/column operations on it, obtaining matrix B.
Are there any unique properties of matrix B that would be the same as matrix A? Such that I will be able to recognize that matrix B is a result of these operations performed on matrix A.
Here are some of the stuff that I've managed to find so far:
From Wikipedia, "Elementary row operations do not change the kernel of a matrix" "Elementary column operations do not change the image, but they do change the kernel."
And I've been told on StackOverflow that "if you don't consider scaling a row/column as an elementary operation a lot more structure is maintained".