 Hi and welcome to the session. I am Shashi. Let us do one question. Question is for the matrices a and b verify that transpose of a b is equal to v transpose a transpose where a is equal to matrix 1 minus 4 3 and b is equal to matrix minus 1 2 1. Let us understand the k-idea to solve the given question. If a is equal to aij b and m into n matrix, then the matrix obtained by interchanging the rows and columns of a is called transpose of a. The transpose of matrix a is denoted by a dash. In other words, if a is equal to matrix aij of the order m into n, then a dash that is a transpose is equal to aij matrix of the order n into m. Let us start with the solution now. We know a is equal to matrix 1 minus 4 3 and b is equal to matrix minus 1 2 1. We can see a is the matrix of order 3 into 1 as it is having three rows and one column and b is the matrix of order 1 into 3 as it is having one row and three columns. Now since the number of columns of a is equal to number of rows of b, so a b is defined. So a b is equal to matrix 1 minus 4 3 multiplied by matrix minus 1 2 1. The matrix a b would be of the order 3 into 3. We get 1 multiplied by minus 1. Then second element of the first row is 1 multiplied by 2. Third element of the first row is 1 multiplied by 1. Then first element of second row is minus 4 multiplied by minus 1. Second element of second row is minus 4 multiplied by 2. Third element of second row is minus 4 multiplied by 1. Now first element of third row is 3 multiplied by minus 1. Second element of third row is 3 multiplied by 2 and third element of third row is 3 multiplied by 1. So we get a b A is equal to matrix minus 1, 2, 1, 4, minus 8, minus 4, minus 3, 6, 3. Now we can find transpose of A B by interchanging the rows and columns of A B. So we get minus 1, 4, minus 3, 2, minus 8, 6, 1, minus 4, 3. So transpose of A B is equal to matrix minus 1, 4, minus 3, 2, minus 8, 6, 1, minus 4, 3. Now we know A is equal to matrix 1, minus 4, 3 and B is equal to matrix minus 1, 2, 1. This is given in the question. So we can find A transpose by interchanging the rows and columns of A. So we get A transpose equal to 1, minus 4, 3 matrix and B transpose is equal to minus 1, 2, 1 matrix. Now transpose of A is equal to matrix 1, minus 4, 3 is of the order 1 into 3 as it is having one row and three columns and B transpose is a matrix minus 1, 2, 1 of order 3 into 1 since it is having three rows and one column. So the product B dash A dash is defined as the number of rows of transpose of A is equal to number of columns of transpose of B. So now let us calculate B dash A dash or B transpose multiplied by A transpose which is equal to matrix minus 1, 2, 1 multiplied by 1, minus 4, 3. Now we will use multiplication of matrices and calculate B transpose A transpose equal to matrix minus 1 multiplied by 1, minus 1 multiplied by minus 4, minus 1 multiplied by 3, then 2 multiplied by 1, 2 multiplied by minus 4, 2 multiplied by 3, 1 multiplied by 1, 1 multiplied by minus 4, 1 multiplied by 3. Now B transpose A transpose is equal to matrix minus 1, 4, minus 3, 2, minus 8, 6, 1, minus 4, 3. So B transpose A transpose is equal to matrix minus 1, 4, minus 3, 2, minus 8, 6, 1, minus 4, 3. But this matrix is equal to A B whole transpose as we can see it from here. So we can write it is equal to transpose of A B. So therefore our required answer is transpose of A B is equal to B transpose A transpose. Hence verify this complete session. Goodbye and take care.