 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. The question is using elementary transformations, find the inverse of each of the matrices. If it exists, the given matrix is 3 minus 1 minus 4 2. Let us now start with the solution. Let A is equal to matrix 3 minus 1 minus 4 2. Now to find inverse by row transformation method, we will write A is equal to I A or 3 minus 1 minus 4 2 is equal to matrix 1 0 0 1 multiplied by A. Now we will apply sequence of row operation simultaneously on matrix A on the left hand side and the matrix I on the right hand side till we obtain I on the left hand side. That is we have to obtain the identity matrix on the left hand side. Now we have to make the diagonal elements of this matrix equal to 1 and all other elements equal to 0. So to make this element equal to 1, we will apply on R 1 row operation 1 upon 3 R 1. So we will write applying R 1 row operation 1 upon 3 R 1 to get the matrix 1 minus 1 upon 3 minus 4 2 is equal to matrix 1 upon 3 0 0 1 multiplied by A. To make this element equal to 0, we will apply on R 2 row operation R 2 plus 4 R 1. So we will write applying on R 2 row operation R 2 plus 4 multiplied by R 1. So we get the matrix 1 minus 1 upon 3 0 2 upon 3 is equal to matrix 1 upon 3 0 4 upon 3 1 multiplied by A. Now make this element equal to 1. We will apply on R 2 row operation 3 upon 2 R 2. So we can write applying on R 2 row operation 3 upon 2 R 2 we get matrix 1 0 minus 1 upon 3 1 is equal to matrix 1 upon 3 0 2 3 upon 2 multiplied by A. Now to make this element equal to 0, we will apply on R 1 row operation R 1 plus 1 upon 3 R 2. So we get applying on R 1 row operation R 1 plus 1 upon 3 R 2 we get matrix 1 0 0 1 is equal to matrix 1 1 upon 2 2 3 upon 2 multiplied by A. We know that identity matrix is equal to A inverse multiplied by A. Clearly this is the identity matrix. So comparing these two equations we get A inverse is equal to this matrix. So we can write A inverse is equal to matrix 1 1 upon 2 2 3 upon 2. So our required inverse is given by the matrix 1 1 upon 2 2 3 upon 2. This completes the session. Hope you enjoyed the session. Goodbye.