 Welcome to the session. I am Shashi and I am going to help you to solve the following question. The question is, using elementary transformations, find the inverse of each of the matrices. If it exists, the given matrix is 2, 1, 1, 1. First of all, let us understand the key idea to solve the given question. We can use either row transformation or column transformation to find the inverse of matrix. Now, to find A inverse, that is the inverse of matrix A, using row transformation, write A is equal to IA and perform the row operations on this expression till we get I is equal to BA. Then, B will be the inverse of A. Let us now start with the solution. First of all, let us assume A is equal to matrix given in the question that is 2, 1, 1, 1. Now, to use row transformation method to find A inverse, we can write A is equal to IA where I is the identity matrix or we can write matrix 2, 1, 1, 1 is equal to matrix 1, 0, 0, 1. Multiply by A. Now, we will perform a sequence of row operations on the matrices A and I, the identity matrix on the left-hand side. The row operations will take place simultaneously on the matrix A on the left-hand side and the matrix I on the right-hand side. Now, first of all, to make this element equal to 1, we will apply on R1, row operation 1 upon 2 R1. So, we can write applying row operation 1 upon 2 R1. We get 1, 1 upon 2, 1, 1 matrix is equal to 1 upon 2, 0, 0, 1 multiplied by A. Now, we know in identity matrix, all elements are 0 except the diagonal elements which are equal to 1. Now, to make this element equal to 0, we will apply on R2, row operation R2 minus R1. So, we can write applying row operation R2 minus R1. We get 1, 1 upon 2, 0, 1 upon 2 is equal to 1 upon 2, 0, minus 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 row operation 2 R2, we get 1, 1 upon 2, 0, 1 is equal to 1 upon 2, 0, minus 1, 2 multiplied by A. Now, to make this element equal to 0, we will apply on R1, row operation R1 minus 1 upon 2 R2. So, we can write applying on R1, row operation R1 minus 1 upon 2 R2. We get matrix 1, 0, 0, 1 is equal to matrix 1, minus 1, minus 1, 2 multiplied by A. Really, this is an identity matrix of the order 2 into 2. So, we can write R is equal to A inverse multiplied by A. Now, comparing the two expressions, we get A inverse is equal to this matrix. So, we can write A inverse is equal to matrix 1, minus 1, minus 1, 2. So, our required inverse is given by the matrix 1, minus 1, minus 1, 2. This is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.