 Hello and welcome to the session. In this session we discuss the following question which says using elementary row operations, find the inverse of the following matrix. This is the matrix of order 2 by 2 with elements 2, 5, 1, 3. Let's proceed with the solution now. Consider the given matrix as A. So matrix A is equal to matrix with elements 2, 5, 1, 3. Now to find the inverse using the elementary row operations, we will write this matrix A as and apply a sequence of row operations on A is equal to IA till we get I equal to BA. And so this matrix B would be the inverse of matrix A. So this gives us matrix A with elements 1, 3 is equal to I that is the identity matrix of order 2 by 2 with the diagonal elements as 1 and rest of the elements as 0 into A. Now we apply the elementary row operations. First we apply and then applying this we get. Now R1 as R1 minus R2 means that the elements in the first row are given by subtracting the elements of the first row and the second row. So this 2 would be replaced by 2 minus 1 which is 1. This 5 is replaced by 5 minus 3 which is N3 which are the elements of the second row remain as it is. And so this matrix is equal to again we apply the same operation to this matrix also the elements of the first row and the second row. So this 1 is replaced by 1 minus 0 which is 1. The 0 is replaced by 0 minus 1 which is minus 1 and 0 and 1 remain as it is. And this matrix into A. Now next operation and applying this we get by subtracting the elements of the first row from the elements of the second row which is this operation. So the elements of the first row remain as it is that is 1 and 2. Now this 1 which is the element of the second row is replaced by 1 minus 1 which is 0. 3 is replaced by 3 minus 2 that is 1 equal to the matrix obtained by applying this operation. So 1 and minus 1 which are the elements of the first row remain as it is. 0 is replaced by 0 minus 1 which is minus 1. This 1 is replaced by 1 minus of minus 1 that is close to make this matrix the identity matrix. So we will apply another row operation. So applying the operation this 1 would be replaced by 1 minus 0 that becomes 1. Then this 2 which is the second element of the first row is replaced by 0. And the 0 and 1 the elements of the second row remain as it is and this is equal to a matrix. The elements of the first row are obtained by this operation. So 1 is replaced by which is 3. Then this minus 1 is replaced by as it is that is minus 1 and 2. This matrix into to obtain this to get the inverse of the matrix A. So we have got the identity matrix is equal to this would be A inverse into therefore we say the matrix with elements 3 leads to the equation. Hope you understood the solution of this question.