Sir,by applying different steps I  am getting different inverses of the same matrix.Please give a proper algorithm for for finding inverse by elementary transformations. 

Hi!

Here is the answer to your question.

 

 

The following algorithm can be used to find the inverse of the square matrix of order 3 × 3 by elementary transformation.

Step1. Introduce 1 at that the (1, 1)^th place.

Step 2. After introducing 1 at (1, 1)^th place introduce 0 at all other places in the 1^st column.

Step 3. Inroduce 1 at the (2, 2)^th place.

Step 4. After introducing 1 at (2, 2)^th place introduce 0 at all other places in the 2^nd column.

Step 5. Introduce 1 at the (3, 3)^th place.

Step 6. After introducing 1 at (3, 3)^th place introduce 0 at all other places in the 3^rd column.

 

Let A = I A 

Applying these steps on matrix A on the the LHS and on matrix I on the RHS, changes the matrix A on the the LHS into an identity matrix and the matrix I on the RHS into inverse of the matrix A.

 

Best Wishes!