Elimination matrix

The entire collection of all the simple row operations we perform to change a matrix into reduced row-echelon form can be brought together in one matrix, and we call that matrix the elimination matrix, (елементарна матрица).

Proof that is square

Example

Performing simple row operations on to get it to reduced row-echelon form:

Representing the row operations with matrices, using :

To get the elimination matrix, multiply :