In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field.

When elementary operations are carried out on identity matrices they give rise to so-called elementary matrices. Definition A matrix is said to be an elementary matrix if and only if it is obtained by performing an elementary (row or column) operation on the identity matrix.

An n × n matrix E qualifies as an elementary matrix if it can be derived from the identity matrix I n by performing a singular row operation. These operations encompass actions such as interchanging two rows, multiplying a row by a scalar factor, or adding one row to another.

In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation (or column operation). Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations.

Elementary Matrix : An elementary matrix is one that may be created from an identity matrix by executing only one of the following operations on it – R1 – 2 rows are swapped. R2 – Multiply one row’s element by a non-zero real number. R3 – Adding any multiple of the corresponding elements of another row to the elements of one row.