 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question is, using elementary transformations, find the inverse of each of the matrices. If it exists, the given matrices 3, 1, 5, 2. Let us start with the solution now. First of all, let us assume A is equal to matrix 3, 1, 5, 2. Now to find the inverse by row transformation method we will write A is equal to I A or we can write matrix 3, 1, 5, 2 is equal to matrix 1, 0, 0, 1 multiplied by A. Now we will apply sequence of row operations simultaneously on matrix A on left hand side and the matrix I on right hand side till we obtain identity matrix on the left hand side. To make this element equal to 1 we will apply on R 1 row operation 1 upon 3 R 1. So we can write applying on R 1 row operation 1 upon 3 R 1 we get 1 upon 3 I 2 matrix is equal to matrix 1 upon 3 0 0 1 multiplied by A. Now to make this element equal to 0 we will apply on R 2 row operation R 2 minus 5 R 1. So we can write applying on R 2 row operation R 2 minus 5 R 1 we get matrix 1 1 upon 3 0 1 upon 3 is equal to matrix 1 upon 3 0 minus 5 upon 3 1 multiplied by A. Now to make this diagonal element equal to 1 we will apply on R 2 row operation 3 R 2. So we can write applying on R 2 row operation 3 R 2 we get matrix 1 1 upon 3 0 1 is equal to matrix 1 upon 3 0 minus 5 3 multiplied by A. Now to make this element equal to 0 we will apply on R 1 row operation R 1 minus 1 upon 3 R 2. So we can write applying on R 1 row operation R 1 minus 1 upon 3 R 2 we get 1 0 0 1 matrix is equal to matrix 2 minus 5 minus 5 3 multiplied by A. Also we can write I is equal to A inverse multiplied by A. Now clearly this is an identity matrix. 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 minus 1 minus 5 3. So the required inverse is given by the matrix 2 minus 1 minus 5 3. This completes the session. Hope you understood the session. Take care and goodbye.