 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that if A is equal to the matrix containing elements 3, 1, x2 and B is equal to matrix containing elements 2, 1, x1 then find the value of x if A square is equal to 5B. We are given A square is equal to 5B. So we first find A square which is equal to A into A that is equal to matrix containing elements 3, 1, x2 into the same matrix containing elements 3, 1, x2. Now when we multiply these two matrices we obtain a 2 by 2 matrix whose elements are the element in the first row first column is 3 into 3 plus x into 1. The element in the first row second column is 3 into x plus x into 2. Now the element in the second row first column is 1 into 3 plus 2 into 1 and the element in the second row second column is 1 into x plus 2 into 2. This is equal to the matrix containing elements 9 plus x 3 plus 2, 3x plus 2x and x plus 4 which is equal to the matrix containing elements 9 plus x 5, 5x x plus 4. Also 5B is equal to 5 into the matrix containing elements 2, 1, x1. Now if we multiply a scalar by a matrix then the scalar has to be multiplied by every element of the matrix. So we obtain this is equal to the matrix containing elements 5 into 2, 5 into x, 5 into 1 and 5 into 1 which is equal to the matrix containing elements 10, 5, 5x and 5. So as a square is equal to 5B we will have matrix containing elements 9 plus x 5, 5x and x plus 4 is equal to the matrix containing elements 10, 5, 5x and 5. As we know if two matrices are equal then their corresponding elements are also equal so we have the equation 9 plus x is equal to 10 which implies x is equal to 10 minus 9 which is equal to 1. So we have x is equal to 1 if a square is equal to 5B which is our answer. This completes the session. Hope you enjoyed the session.