 Hi and welcome to the session. I'm Shashi. Let us do one question. Question is if a is equal to matrix 3, 1, minus 1, 2, show that a square minus 5a plus 7i is equal to 0. Let us now start with the solution. We are given a is equal to matrix 3, 1, minus 1, 2. Now to prove the equation a square minus 5a plus 7i equal to 0, we will first find out a square. So we know a square is equal to a multiplied by a. So we know matrix a is 3, 1, minus 1, 2, multiplied by matrix 3, 1, minus 1, 2. Now we can see both the matrices are square matrices of the same order. So their product is defined. So applying the multiplication of the matrices we get the matrix 9 minus 1, 3 plus 2, minus 3, minus 2, minus 1, plus 4. On simplifying we get a square is equal to matrix 8, 5, minus 5, 3. Now the next term of the equation is minus 5a. So we will find minus 5a now. So we can write minus 5a is equal to minus 5 multiplied by matrix 3, 1, minus 1, 2. Now this is equal to minus 15, minus 5, 5, minus 10 matrix. So minus 5a is equal to matrix minus 15, minus 5, 5, minus 10. We had multiplied every element of the matrix a with minus 5. We know minus 5 into 3 is equal to minus 15, minus 5 into 1 is minus 5. Similarly we can multiply other two elements with minus 5 and get the required matrix. Now next term of the equation is 7i. So we will find out 7i now where i is the identity matrix. Clearly we can see 7i is equal to 7 multiplied by the identity matrix of order 2 into 2. So we get 7i is equal to matrix 7, 0, 0, 7. Now we can write the equation a square minus 5a plus 7i equal to a square plus minus 5a plus 7i. So we can write a square minus 5a plus 7i is equal to a square is equal to matrix 8, 5, minus 5, 3 plus minus 5a is equal to matrix minus 15, minus 5, 5, minus 10 and 7i is equal to matrix 7, 0, 0, 7. Now we will add the three matrices and get 8 minus 15 plus 7, 5 minus 5 plus 0, minus 5, plus 5, plus 0, 3 minus 10, plus 7. Now this is further equal to matrix 0, 0, 0, 0. Clearly this is a 0 matrix as all the elements in the matrix are equal to 0. So we can denote it by 0. As we know 0 matrix can be denoted by 0. So our required answer is a square minus 5a plus 7i is equal to 0. Hence, proved. This completes the session. Have a nice day. Goodbye.