 Hi, I am Meenu and we are discussing this question. It says if A is this 2 x 2 matrix, show that A square minus 5A minus 14 is 0. So let's proceed on to the solution. We have to prove that A square minus 5A minus 14I, where I is the 2 x 2 identity matrix and we have to find A square and 5A. Now A is 3 minus 4 minus 5 2, therefore A square is minus 4 minus 5 2, multiplying the 2 3 into 3 plus minus 5 into minus 4 and 3 into minus 5 plus minus 5 into 2, then minus 4 into 3 plus 4 into 2 into minus 4, 2 into minus 4, then minus 4 into minus 5 plus 2 into 2, which is equal to 339 plus 2029 minus 15 minus 10 is minus 25 minus 12 minus 8 is minus 20, 20 plus 4 is 24. So this is A square. We now find 5A. To obtain 5A we need to multiply A with 5. So we multiply each term of matrix A with 5. So we get 15 minus 25 minus 20 and 10. Now we have to find 14I. I is the 2 x 2 identity matrix. So 14I becomes 14, 0, 0, 14. Now A square minus 5A minus 14I is equal to A square is 29 minus 25 minus 20, 24 minus 5A minus 5A is 15 minus 25 minus 20, 10 minus 14, 0, 14, which is equal to 14, not 29 minus 15 is 14, minus 25 plus 25 is 0, minus 20 plus 20 is 0, 24 minus 10 is 14. We have subtracted 5A from A square. Now this is equal to 0, 0, matrix 0, 14 minus 0, 14 minus 14 is 0, 0 minus 0 is 0 and so on. Hence A square minus 5A minus 14 is equal to 0. A square minus 5A minus 14I is equal to 0. 0 means the 0 matrix. So this is proved now. So by far now, take care. Hope you enjoyed the session.