Elementary Transformations or Elementary Operations of a Matrix

1. Interchange of two rows or columns.
2. Multiplication of all elements of a row or column of a matrix by a non-zero scalar,
3. Addition to the elements of a row or column of the corresponding elements of any other row (to a row) or any other column (to a column) multiplied by a scalar k.


Elementary matrix: A matrix obtained from an identity matrix by a single elementary operation (transformation) is called an elementary matrix.