 Hello and welcome to the session. In this session we discuss the following question which says if A is equal to the matrix with elements cos alpha minus sin alpha sin alpha cos alpha then for what value of alpha is A an identity matrix. Before moving on to the solution we will discuss what an identity matrix is. Consider a square matrix A equal to A ij which is an n by n on the matrix. So this A is an identity matrix if we have the elements of the square matrix A given by A ij would be 1 where i is equal to j that is the diagonal elements are 1 and rest of the elements are 0. So when this condition is satisfied then we say that the square matrix A is an identity matrix that is a square matrix in which all the elements in the diagonal are 1 and rest of the elements are 0 and we denote the identity matrix by i. Since the square matrix A is an identity matrix so A is equal to i this is the key idea that we use for this question. Let us now proceed with the solution we have given a square matrix A with elements cos alpha i alpha in the first form sin alpha cos alpha in the second form and we are supposed to find the value of alpha such that the square matrix A is an identity matrix. Now the square matrix A is an identity matrix so this would mean that the matrix with elements cos alpha minus sin alpha in the first form in alpha cos alpha in the second form is equal to the matrix of order 2 by 2 with the diagonal elements as 1 and the rest of the elements as 0. Now equating the elements of these two matrices we have cos alpha would be equal to 1 then the sin alpha would be equal to 0 cos alpha equal to 1 gives us alpha equal to 0 and also sin alpha equal to 0 gives us alpha equal to 0. Therefore we have the value of alpha as 0 which is our final answer this completes the equation for p r distributed solution of this question.