 Hi, and welcome to the session. I'm Shashi. Let us do one question. Question is, choose the correct answer in the following questions. If a is equal to matrix alpha beta gamma minus alpha, it's such that a squared is equal to i, where i is the identity matrix. Then a, 1 plus alpha squared plus beta gamma is equal to 0. b, 1 minus alpha squared plus beta gamma is equal to 0. c, 1 minus alpha squared minus beta gamma is equal to 0. d, 1 plus alpha squared minus beta gamma is equal to 0. We have to choose the correct answer. Let us now start with the solution. We know a is equal to matrix alpha beta gamma minus alpha. And we know a squared is equal to a modified by a. So we can write alpha beta gamma minus alpha multiplied by alpha beta gamma minus alpha. Both matrix are square matrix of same order, so their multiplication is defined. So on multiplying both the matrices, we get matrix alpha squared plus beta gamma alpha beta minus alpha beta gamma alpha minus gamma alpha beta gamma plus alpha squared. On simplifying further, we get a squared is equal to alpha squared plus beta gamma alpha beta minus alpha beta is equal to 0. Similarly, gamma alpha minus gamma alpha is equal to 0. And last element is alpha squared plus beta gamma. Now we are given in the question that a squared is equal to i, where i is the identity matrix. So we can write a squared is equal to this matrix. So alpha squared plus beta gamma 0 alpha squared plus beta gamma is equal to matrix 1, 0, 0, 1, that is identity matrix. So on comparing the corresponding elements of the matrices, we get alpha squared plus beta gamma must be equal to 1. This further implies 1 minus alpha squared minus beta gamma is equal to 0. So our required answer is c. As the equation in the c part is 1 minus alpha squared minus beta gamma is equal to 0, which is same as we have obtained in the answer. So c is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.