 Hi and welcome to the session. I am Shashi. Let us do one question. Question is if a is equal to matrix cos alpha minus sin alpha sin alpha cos alpha then a plus a transpose is equal to i where i is the identity matrix. If the value of alpha is a pi upon 6 b pi upon 3 c pi d 3 pi upon 2. Here we have to choose the correct answer. Let us now start with the solution. We know a is equal to matrix cos alpha minus sin alpha sin alpha cos alpha. Now we can find a transpose by interchanging the rows and columns of a. So a transpose is equal to cos alpha sin alpha minus sin alpha cos alpha. Now we have to find a plus a transpose. So a plus a transpose is equal to matrix a that is cos alpha minus sin alpha sin alpha cos alpha plus matrix a transpose that is cos alpha sin alpha minus sin alpha cos alpha. Now we will add the corresponding elements of the two matrices. So we get a plus a transpose is equal to cos alpha plus cos alpha is cos alpha minus sin alpha plus sin alpha is 0 sin alpha plus minus sin alpha is again 0 cos alpha plus cos alpha is 2 cos alpha. So a plus a transpose is equal to matrix 2 cos alpha 0 0 2 cos alpha. Now according to the question a plus a transpose is equal to i. So the matrix 2 cos alpha 0 0 2 cos alpha must be equal to matrix 1 0 0 1. So this can only be possible if 2 cos alpha is equal to 1 or cos alpha is equal to 1 upon 2. Now this further implies cos alpha is equal to cos pi upon 3. We know cos pi upon 3 is equal to 1 upon 2. So we substitute cos pi upon 3 in place of 1 upon 2. So this implies alpha is equal to pi upon 3. So value of alpha is equal to pi upon 3. So our required answer is b. Hence correct answer is b. This is the required answer. Hope you enjoyed the session. Take care and goodbye.