 Hi and welcome to the session. I am Shashi. Let us do one question. Question is, if A transpose is equal to matrix 3 4 minus 1 2 0 1 and B is equal to matrix minus 1 2 1 1 2 3 then verify that A minus B whole transpose is equal to A transpose minus B transpose. First recall, let us understand the key idea to solve the given question. If A is equal to matrix A ij Bn m into n matrix then the matrix obtained by interchanging the rows and columns of A is called transpose of A. The transpose of the matrix A is denoted by A dash. In other words, if A is equal to matrix A ij of the order m into n then A dash that is A transpose is equal to matrix A ij of the order n into m. Let us now start with the solution. A transpose given to us in the question is matrix 3 4 minus 1 2 0 1. We also know that A is equal to transpose of A transpose. So, to find A we will find the transpose of A transpose. Now transpose of A transpose is equal to matrix 3 4 minus 1 2 0 1. We have interchanged the rows and columns of A transpose to obtain the transpose of A transpose. We can see the first row of A transpose has become the first column of transpose of A transpose. Second row of A transpose is the second column of transpose of A transpose and the third row of A transpose is the third column of transpose of A transpose. So, you know transpose of A transpose is equal to A. So, A is equal to matrix 3 minus 1 0 4 2 1. Now, being given to us in the question is equal to matrix minus 1 2 1 1 2 3. Now we will obtain minus B minus B is equal to matrix 1 minus 2 minus 1 minus 1 minus 2 minus 3. Right? To obtain minus B we had multiplied all the elements of matrix B with minus 1. Now we know A minus B is equal to A plus minus B. So, we can write A minus B is equal to matrix 3 minus 1 0 4 2 1 plus matrix 1 minus 2 minus 1 minus 1 minus 2 minus 3. Now to add both the matrices we will add the corresponding elements of both the matrix. 3 plus 1 is equal to 4 minus 1 plus minus 2 is equal to minus 3. 0 plus minus 1 is equal to minus 1. 4 plus minus 1 is 3. 2 plus minus 2 is 0. 1 plus minus 3 is minus 2. So, we obtain A minus B is equal to matrix 4 minus 3 minus 1 3 0 minus 2. Now to obtain transpose of A minus B we will interchange the rows and columns of A minus B. So, we get 4 minus 3 minus 1 3 0 minus 2. A minus B transpose is equal to 4 3 minus 3 0 minus 1 minus 2 matrix. Now A transpose is equal to matrix 3 4 minus 1 2 0 1 is already given in the question and matrix B is equal to minus 1 2 1 and 1 2 3. So, this is also given in the question. Now we will find out B transpose. B transpose is obtained by interchanging the rows and columns of B. So, we get minus 1 2 1 1 2 3. So, B transpose is equal to minus 1 1 2 2 1 3 matrix. Now for obtaining minus B transpose we will multiply all the elements of B transpose with minus 1. So, we get 1 minus 1 minus 2 minus 2 minus 1 minus 3 . So, minus B transpose is equal to matrix 1 minus 1 minus 2 minus 2 minus 1 minus 3. Now we have to find A transpose minus B transpose. It can be written as A transpose plus minus B transpose. So, we know A transpose given in the question is 3 4 minus 1 2 0 1 2 3 minus 1 and minus B transpose we have already obtained above is 1 minus 1 minus 2 minus 2 minus 1 minus 3. Now we get A transpose minus B transpose is equal to 3 plus 1 is 4 plus minus 1 is 3 minus 1 plus minus 2 is minus 3 2 plus minus 2 is 0 0 plus minus 1 is minus 1 1 plus minus 3 is minus 2. So, A transpose minus B transpose is equal to matrix 4 3 minus 3 0 minus 1 minus 2. But this matrix is same as matrix obtained for A minus B whole transpose as we can see here clearly. So, we can write it equal to A minus B whole transpose. So, our required answer is A minus B whole transpose is equal to A transpose minus B transpose. Hence, verified. This completes the session. Hope you understood the session. Take care and goodbye.