 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, the given matrix is 2513. Let us now start with the solution. First recall, let us assume a is equal to matrix 2513. Now to find the inverse by no transformation method, let us write a is equal to i8 where i is the identity matrix. Or we can write matrix 2513 is equal to matrix 1001 multiplied by 8. Now we will apply sequence of flow operations simultaneously on matrix A on left hand side and the matrix I on right hand side. Till we obtain identity matrix on left hand side. Now to make this element equal to 1, we will apply on R1 row operation 1 upon 2 R1. So we can write, applying on R1 row operation 1 upon 2 R1 we get 15 upon 2 13 is equal to matrix 1 upon 2 001 multiplied by 8. Now to make this element equal to 0, we will apply on R2 row operation R2 minus R1. So we can write, applying on R2 row operation R2 minus R1 we get 15 upon 2 0 1 upon 2 is equal to matrix 1 upon 2 0 minus 1 upon 2 1 multiplied by 8. 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 15 upon 2 01 is equal to matrix 1 upon 2 0 minus 1 2 multiplied by 8. Now to make this element equal to 0, we will apply on R1 row operation R1 minus 5 upon 2 R2. So we can write applying on R1 row operation R1 minus 5 upon 2 R2 we get 1 001 matrix is equal to 3 minus 5 minus 1 2 matrix multiplied by 8. Now you also know that I is equal to A inverse multiplied by 8. Now this is an identity matrix. Now comparing the two expressions we can clearly see A inverse is given by this matrix. So we can write A inverse is equal to matrix 3 minus 5 minus 1 2. The required inverse is given by the matrix 3 minus 5 minus 1 2. This completes the session. Hope you understood the session. Take care and goodbye.