 Hi and welcome to the session. I am Shashi. Let us do one question. Question is for the matrix A is equal to matrix 1567, verify that A plus A transpose is a symmetric matrix. First of all, let us understand that a square matrix B is said to be symmetric if B transpose is equal to B or we can say the transpose of a matrix is equal to itself. This is the key idea to solve the given question. Let us now start with the solution. We have given A is equal to matrix 1567. Now we will find out A transpose by interchanging rows and columns of A. So we get 1657 as A transpose. Now we will find A plus A transpose. So we can write A plus A transpose is equal to matrix 1567 plus matrix 1657. Now adding corresponding elements of the two matrices we get 1 plus 1 is 2, 5 plus 6 is 11, 6 plus 5 is 11, 7 plus 7 is equal to 14. So we get A plus A transpose is equal to matrix 211114. Now we will find out transpose of A plus A transpose that is equal to 211114. Transpose of A plus A transpose can be obtained by interchanging the rows and columns of the matrix A plus A transpose. So here we can see transpose of A plus A transpose is equal to A plus A transpose as the matrices for both are same. So we can write A plus A transpose whole transpose is equal to A plus A transpose. Now this condition shows that A plus A transpose is a symmetric matrix. So we can write A plus A transpose is a symmetric matrix. As we have already read in key idea that if transpose of a matrix is equal to itself then it is a symmetric matrix. This completes the session. Hope you understood the session. Take care and goodbye.