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```Elementary Operations of a Matrix

The following three operations applied on the rows (columns) of a matrix are called elementary row (column) transformations.

(i) Interchange of any two rows (columns)

If ith row (column) of a matrix is interchanged with the jth row (column), it will be denoted by Ri ↔ Rj (Ci ↔ Cj).

For example: A = , then by applying R1 → R2 we get B = .

(ii) Multiplying all elements of a row (column) of a matrix by a non-zero scalar. If the elements of ith row (column) are multiplied by non-zero scalar k, it will be denoted by Rl→Ri (k) [Ci→Ci (k)] or Rl→kRi [Ci→kCi].

If A = , then by applying R2 → 3R2, we obtain B = .

(iii) Adding to the elements of a row (column), the corresponding elements of any other row (column) multiplied by any scalar k.

If k times the elements of jth row (column) are added to the corresponding elements of the ith row (column), it will be denoted by Ri→Ri + k Rj (Ci→Ci + kCj).

If A=, then application of elementary operation R3→R3 + 2R1 lead to B =.

Illustration:

Using elementary row transformations and find the inverse of the matrix A= .

Solution:

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