Finding inverse of 3x3 matrix using elementary transformation

We shall learn the process of finding inverse of 3x3 matrix using elementary transformation . The  method of finding inverse of the matrix 3 x 3 using elementary row transformations involves 5 to 6 steps . Let us understand this method with the help of an example.

Inverse of 3x3 matrix using elementary transformation

For finding Inverse of  3 x 3 Matrix using Elementary Row Transformations , We shall strat with this formula

  A  = I A ,

 Where I is Unit Matrix of order 3

In the 1st step we have to make 1st element of 1st row and 1st column unity. We shall start changing the given matrix written  in left hand side  step by step to unit matrix and this this process will also appliesd to the the unit matrix written on right hand side of equation (1) , Hence this change the  matrix written on the right hand side of  equation (1) to other matrix . And when the given matrix on the left hand side changed to Unit matrix , the matrix which was on the right hand side of equation of (1) will be inverse of the given matrix.

Suggested direction of elementary rows operations  are as follows

In the 1st step we have to make the 1st element of 1st column to unity by using taking suitable number common from it .

In the next step by using the above step we have to make 2nd and 3rd  element of 1st column unity by using suitable row transformations. 

 

Till now we have made two elements of 1st column zero , now we have to make 1st and 2nd elements of 3rd Row zero by using suitable row elementary transformations. Note carefully 3rd elements of 3rd row can not be changed to zero as this element will have to  be reduced to unity as in Unit Matrix. 

After this step start making the elements of 2nd Row equal to zero but using suitable row transformations.

Now we shall conclude the process of inverse of matrix  with the changing of  2nd and 3rd elements of 1st row  to zero.. 

Here matrix B is the inverse of the given matrix A. 

To verify that the matrix B obtained is correct or not. We can check it by multiplying matrix B with I, if it comes out equal to matrix A. Then our answer is correct. 

Also read this Post for solution of set of three variables equations using matrix method

So the process of finding inverse of 3x3 matrix using elementary transformation discussed in this post with the help of an example. Your comment will always be appreciated for betterment of this blog.