 Hello friends, welcome to the session. I am Malka. We are going to discuss matrices. Our given question is fine, a square minus 5 a plus 6 i if a equal to matrix 2, 0, 1, 2, 1, 3, 1 minus 1, 0. Now let's start with the solution. We are given a equal to matrix 2, 0, 1, 2, 1, 3, 1, minus 1, 0. Now first of all we will calculate the value of a square. Therefore a square equal to 2, 0, 1, 2, 1, 3, 1, minus 1, 0 is multiplied by a which is 2, 0, 1, 2, 1, 3, 1, minus 1, 0. So this is equal to on multiplying first row with the first column we get 2 cross 2 plus 0 cross 2 plus 1 cross 1 then 2 into 0 plus 0 into 1 plus 1 into minus 1, 2 into 1 plus 0 into 3 plus 1 into 0, 2 into 2 plus 1 into 2 plus 3 into 1 then 2 into 0 plus 1 into 1 plus 3 into minus 1, 2 into 1 plus 1 into 3 plus 3 into 0. Similarly for the last row 1 into 2 plus minus 1 into 2 plus 0 into 1, 1 into 0 minus 1 into 1 plus 0 into minus 1, 1 into 1 minus 1 into 3 plus 0 into 0. This is equal to matrix 4 plus 0 plus 1, 0 plus 0 minus 1, 2 plus 0 plus 0, 4 plus 2 plus 3, 0 plus 1 minus 3, 2 plus 3 plus 0, 2 minus 2 plus 0, 0 minus 1 plus 0, 1 minus 3 plus 0. This is equal to 5 minus 1, 2, 9, minus 2, 5, 0 minus 1, minus 2. So this is the value of a squared. Now we will find the value of minus 5 a minus 5 a equal to minus 5 into matrix a which is 2, 0, 1, 2, 1, 3, 1, minus 1, 0. So this is equal to minus 10, 0, minus 5, minus 10, minus 5, minus 15, minus 5, plus 5 and 0. So this is the value of minus 5 a. Now we find the value of 6i. 6i equal to 6 into identity matrix of order 3, 1, 0, 0, 0, 1, 0, 0, 0, 1. This is equal to 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6. Now, we will substitute the value of a square minus 5a and 6i, this will give us therefore a square minus 5a plus 6i equal to 5 minus 1 to 9 minus 2 5 0 minus 1 minus 2 then minus 5a which is minus 10 0 minus 5 minus 10 minus 5 minus 5 5 minus 15 0 plus 6i which is 6 0 6 0 0 0 6. So, this is equal to 5 minus 10 plus 6 minus 1 plus 0 plus 0 2 minus 5 plus 0 9 minus 10 plus 0 minus 2 minus 5 plus 6 5 minus 15 plus 0 0 minus 5 plus 0 minus 1 plus 5 plus 0 minus 2 plus 0 plus 6 this is equal to matrix 1 minus 1 minus 3 minus 1 minus 1 minus 10 minus 5 4 and 4. So, therefore a square minus 5a plus 6i equal to matrix 1 minus 1 minus 3 minus 1 minus 1 minus 10 minus 5 4 4. So, this is the answer hope you understood the solution and enjoy the session goodbye and take care.