 Hi, and welcome to the session. Let's work out the following question. The question says if a is equal to the matrix 3 1 minus 1 2, show that a square minus 5 a plus 7 i is equal to 0. So let us start with the solution to this question. Here a is equal to the matrix 3 1 minus 1 2. Now we see that. Now we consider the LHS of this, that is a square minus 5 a plus 7 i. That is equal to, now a square will be the matrix 3 1 minus 1 2 multiplied by 3 1 minus 1 2. Minus 5 into a, that is 3 1 minus 1 2 plus 7 into identity matrix, that is 1 0 0 1. Now this is equal to, here we have 3 3's are 9 plus 1 into minus 1 is minus 1. So 9 minus 1, that is 8. So we have the matrix 8 5 minus 5 3 plus the matrix minus 15 minus 5 5 minus 10 plus the matrix 7 0 0 7. That is further equal to, now 8 minus 15 plus 7 is 0, 5 minus 5 plus 0 is 0, so on we have the matrix 0 0 0 0. That is equal to 0 and that is also the RA chips. So this is what we are supposed to prove. I hope that you understood the solution and enjoyed the session. Have a good day.