 Hi and welcome to the session I am Shashi and I am going to help you to solve the following question. Question is, using elementary transformations find the inverse of each of the matrices if it exists. Given matrix is 2 minus 3 minus 1, 2. Let us start with the solution now. First of all let us assume a is equal to a given matrix in the question that is 2 minus 3 minus 1, 2. Now to find the inverse by elementary row transformation method we will write n is equal to i a where i is the identity matrix. So we can write matrix 2 minus 3 minus 1, 2 is equal to matrix 1, 0, 0, 1 multiplied by a. Now we will perform row operations simultaneously on the matrix a on left hand side and we will write the matrix i on right hand side till we obtain identity matrix on the left hand side. Now to make this element equal to 1 we will apply an R1 row operation 1 upon 2 R1. So we can write applying on R1 row operation 1 upon 2 R1 we get 1 minus 3 upon 2 minus 1, 2 is equal to matrix 1 upon 2, 0, 0, 1 multiplied by a. Now to make this element equal to 0 we will apply on R2 row operation R2 plus R1. So we can write applying on R2 row operation R2 plus R1 we get matrix 1 minus 3 upon 2, 0, 1 upon 2 is equal to matrix 1 upon 2, 0, 1 upon 2, 1 multiplied by a. Now to make this element equal to 1 we will apply on R2 row operation 2 R2. So we can write applying on R2 row operation 2 R2 we get matrix 1 minus 3 upon 2, 0, 1 is equal to matrix 1 upon 2, 0, 1, 2 multiplied by a. Now to make this element equal to 0 we will apply on R1 row operation R1 plus 3 upon 2 R2. So we can write applying on R1 row operation R1 plus 3 upon 2 R2 we get matrix 1, 0, 0, 1 is equal to matrix 2, 3, 1, 2 multiplied by a. Now we have obtained our identity matrix on the left hand side. We know identity matrix is equal to a inverse multiplied by a. Now comparing these two expressions we get a inverse is equal to this matrix. So we can write a inverse is equal to matrix 2, 3, 1, 2. So our required inverse is given by the matrix 2, 3, 1, 2. This completes the session. Hope you understood the session. Take care and goodbye.