 I and welcome to the session. I am Shashi. Let us do one question. Question is, if A is equal to matrix cos alpha sin alpha minus sin alpha cos alpha, then verify that A transpose multiplied by A is equal to I, where I is the identity matrix. First of all, let us understand the KIDR to solve the given question. If A is equal to Aij 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 Aij of the order m into n, then A transpose is equal to matrix Aji of the order n into m. Let us start with the solution now. We know K is equal to matrix cos alpha sin alpha minus sin alpha cos alpha. Now, we can obtain A transpose by interchanging the rows and columns of A. So, we get cos alpha sin alpha minus sin alpha cos alpha. Now, we have to find A transpose A. So, this is equal to matrix cos alpha minus sin alpha sin alpha cos alpha multiplied by the matrix cos alpha sin alpha minus sin alpha cos alpha. After multiplying the two matrices, we get cos alpha multiplied by cos alpha plus minus sin alpha multiplied by minus sin alpha. Now, next second element of the first row is cos alpha multiplied by sin alpha plus minus sin alpha multiplied by cos alpha. First element of the second row is sin alpha multiplied by cos alpha plus cos alpha multiplied by minus sin alpha. Now, next element of the second row is sin alpha multiplied by sin alpha plus cos alpha multiplied by cos alpha. We had multiplied first row with first column for this term, then first row with second column for this term and second row with first column for this term and second row with second column for this term. Now, this matrix is further equal to cos square alpha plus sin square alpha cos alpha sin alpha minus cos alpha sin alpha sin alpha cos alpha minus cos alpha sin alpha sin square alpha plus cos square alpha. Now, we know sin square alpha plus cos square alpha is equal to 1. We will substitute the value of cos square alpha plus sin square alpha equal to 1 and get A transpose A is equal to matrix 1 cos alpha sin alpha minus cos alpha sin alpha would be 0. Similarly, sin alpha cos alpha minus cos alpha sin alpha would also be equal to 0. Then, sin square alpha plus cos square alpha is equal to 1. So, we get A transpose A is equal to matrix 1 0 0 1 which is equal to i. So, we get A transpose A is equal to i. Verify, this is our required solution. This completes the session. Hope you enjoyed the session. Take care and goodbye.