 and welcome to the session I am searching 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 1, 3, minus 2, minus 3, 0, minus 5, 2, 5, 0. Let us start with the solution of let A is equal to matrix 1, 3, minus 2, minus 3, 0, minus 5, 2, 5, 0. Now, to find inverse by row transformation method, we will write A is equal to IA, where I is the identity matrix or we can write matrix 1, 3, minus 2, minus 3, 0, minus 5, 2, 5, 0 is equal to matrix 1, 0, 0, 0, 1, 0, 0, 0, 1 multiplied by A. Now, to make this element equal to 0, we will apply on R2, row operation R2 plus 3 R1. And to make this element equal to 0, we will apply on R3, row operation R3 minus 2 R1. Now, we can write, applying row operation R2 plus 3 R1 and on R3, row operation R3 minus 2 R1. We get the matrix 1, 3, minus 2, 0, 9, minus 11, 0, minus 1, 4 is equal to matrix 1, 0, 0, 3, 1, 0, minus 2, 0, 1 multiplied by A. Now, to make this diagonal element equal to 1, we will apply on R2, row operation 1 upon 9, R2. So, you can write, applying R2, row operation 1 upon 9, R2, we get matrix 1, 3, minus 2, 0, 1, minus 11 upon 9, 0, minus 1, 4 is equal to matrix 1, 0, 0, 0, 0, 0, 0, 0, 1 multiplied by A. To make this element equal to 0, we will apply on R1, row operation R1 minus 3 R2 and to make this element equal to 0, we will apply on R3, row operation R3 plus R2. So, we can write, applying row operation R1 minus 3 R2 and applying on R3, row operation R3 plus R2 we get matrix 1, 0, 5 upon 3, 0, 1, minus 11 upon 9, 0, 0, 25 upon 9, 0 multiplied by A. 1, 9 is equal to matrix 0 minus 1 upon 3 0, 1 upon 3 1 upon 9 0, minus 5 upon 3, 1 upon 9 1 matrix multiplied by 8. Now, to make this element equal to 1, we will apply on R3, row operation 9 upon 25 R3. So, we can write, applying on R3, row operation 9 upon 25 R3, we get matrix 1 0 5 upon 3 0 1 minus 11 upon 9 0 0 1 is equal to matrix 0 minus 1 upon 3 1 upon 9 0 minus 3 upon 5 1 upon 25 9 upon 25, multiplied by 8. Now, to make this element equal to 0, we will apply on R1, row operation R1 minus 5 upon 3 R3 and to make this element equal to 0, we will apply on R2, row operation R2 plus 11 upon 9 R3. So, we can write, applying on R1, row operation R1 minus 5 upon 3 R and on R2, row operation R2 plus 11 upon 9 R3. So, we get the matrix 1 0 0 0 1 0 0 1 is equal to matrix 1 minus 2 upon 5 minus 3 upon 5 minus 2 upon 5 4 upon 25 11 upon 25 minus 3 upon 5 1 upon 25 9 upon 25 multiplied by 8. Now, we have obtained the identity matrix on the left hand side. So, we will stop the elementary row operations here. Now, we know identity matrix is also equal to A inverse multiplied by 8. Really, this is an identity matrix. Comparing these two expressions, we get A inverse is equal to this matrix. So, we can write A inverse is equal to matrix 1 minus 2 upon 5 minus 3 upon 5 minus 2 upon 5 4 upon 25 11 upon 25 minus 3 upon 5 1 upon 25 9 upon 25. So, our required inverse is given by the matrix 1 minus 2 upon 5 minus 3 upon 5 minus 2 upon 5 4 upon 25 11 upon 25 minus 3 upon 5 1 upon 25 9 upon 25. This completes our session. Hope you enjoyed the session. Take care and goodbye.