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 *, *if the *i*th and *j*th rows are interchanged.

**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