 Hi, and welcome to the session. I'm Shashik and I'm going to help you to solve the following question. Question is, find half multiplied by a plus a transpose and half multiplied by a minus a transpose. Then, a is equal to matrix 0 a b minus a 0 c minus b minus c 0. Let us now start with the solution. We know a is equal to matrix 0 a b minus a 0 c minus b minus c 0. Now, we can find a transpose by interchanging the rows and columns of a. So, we get a transpose equal to 0 minus a minus b a 0 minus c b c o. Now, we will add the two matrices to find a plus a transpose. a plus a transpose is equal to matrix 0 a b minus a 0 c minus b minus c 0 plus matrix 0 minus a minus b a 0 minus c b c o. Now, we will add the corresponding elements of the two matrices. Now, a plus a transpose is equal to 0 plus 0 is 0 a plus minus a is 0 b plus minus b is 0 minus a plus a is 0 0 plus 0 is 0 c plus minus c is 0. minus b plus b is 0 minus c plus c is 0 0 plus 0 is 0. Clearly, we can see this is our 0 matrix. So, we get a plus a transpose equal to 0 as we can denote the 0 matrix by 0. Now, half multiplied by a plus a transpose is equal to 0. Now, we know a transpose is equal to matrix 0 minus a minus b a 0 minus c b c o. Now, we will calculate minus a transpose minus a transpose is equal to 0 a b minus a 0 c minus b minus c 0. Here, we have multiplied every element of a transpose with minus 1 to get minus a transpose. Now, we will calculate a minus a transpose. We know a minus a transpose can be written as a plus minus a transpose. So, we know a is equal to matrix 0 a b minus a 0 c minus b minus c 0 and minus a transpose we have already calculated. It is equal to the matrix 0 a b minus a 0 c minus b minus c 0. Now, we will add the corresponding elements of the two matrix. So, we get 0 plus 0 equal to 0 a plus a is equal to 2 a b plus b is equal to 2 b minus a plus minus a is equal to minus 2 a 0 plus 0 is again 0. c plus c is 2 c minus b plus minus b is equal to minus 2 b minus c plus minus c is minus 2 c 0 plus 0 is 0. Now, we can take 2 as a common factor from every element of the matrix a minus a transpose. So, we get a minus a transpose is equal to 2 multiplied by matrix 0 a b minus a 0 c minus b minus c 0. Now, we have to find half multiplied by a minus a transpose. So, we will multiply half with a minus a transpose matrix. So, we get half multiplied by 2 multiplied by matrix 0 a b minus a 0 c minus b minus c 0. 2 and 2 will get cancelled. So, we get the matrix 0 a b minus a 0 c minus b minus c 0. So, half a minus a transpose is equal to matrix 0 a b minus a 0 c minus b minus c 0. So, our final answer is half a plus a transpose is equal to 0 matrix and half a minus a transpose is equal to 0 a b minus a 0 c minus b minus c 0 matrix. This completes the session. Hope you understood the session. Take care and goodbye.