When we apply any of the following operation on a matrix, then we call it an elementary transformation.
1. Interchanging any two rows (or columns). This transformation is indicated by 
2. Multiplication of the elements of any row (or column) by a non-zero scalar quantity k is denoted by (k.
3. Addition of constant multiplication of the elements of any row to the corresponding elements of any other row Rj is denoted by ( + k).
If a matrix B is obtained from a matrix A by one or more E-operations, then B will be equivalent to A. We use the symbol ~ for equivalence.
i.e., A ~ B.
Inverse of a matrix by using el. transformation-
The following transformations are elementary transformations-
1. Interchange of any two rows (column)
2. Multiplication of any row or column by any non-zero scalar quantity k.
3. Addition to one row (column) of another row(column) multiplied by any non-zero scalar.
The symbol ~ we use for equivalence.
Elementary matrices
If we get a square matrix from an identity or unit matrix by using any single el. transformation, we call it an elementary matrix.
Note- Every elementary row transformation of a matrix can affect by pre-multiplication with the corresponding elementary matrix.
The method of finding inverse of a non-singular matrix by using el. transformation-
Working steps-
1. Write A = IA
2. Perform an elementary row transformation of A on the left side and I on the right side.
3. Apply elementary row transformation until ‘A’ (left side) reduces to I, then I reduces to 
Example-1: Find the inverse of matrix ‘A’ by using elementary transformation
Sol. Write the matrix ‘A’ as-
A = IA
Now apply the following operation
So that
Example-2: Find the inverse of matrix ‘A’ by using el. transformation-
Sol. Write the given matrix ‘A’ as-
hence A = IA
So that
