 Welcome to the session. Let us discuss the following question. The question says, if A is equal to this matrix, find x and y, such that A squared plus x into unit matrix is equal to y into A, hence, y, A involves. Now, begin with the solution. We are given A as 2 by 2 matrix in which elements are 3, 1, 7, 5. A squared plus xi is equal to yA. Let's first find out A squared. Now, A squared is equal to this matrix multiplied by x is equal to 2 matrix in which elements are 3 into 3 plus 1 into 7 into 5, 3 plus 5 into 7, 7 into 1 plus 5 into 5. And this is equal to 2 by 2 matrix in which elements are 60, 0, 0, substituting y as equation 3 by minus x equals to 16. This implies 3 into 8 minus x is equal to 60. This implies 24 minus 16 is equal to x. And this implies x is equal to 8. So now our given equation becomes A squared plus 8i is equal to 8A. By multiplying both sides of this equation by A inverse, we get A inverse into A squared plus A i A inverse equals to A A into A inverse. This implies A plus 8A inverse is equal to 8i as A A inverse is equal to 8i. This implies 8A inverse is equal to 8i minus A. This implies A inverse is equal to A into unit matrix minus A that is given matrix. Now we will multiply all elements of this matrix by 8 minus this matrix. Let's now subtract the corresponding elements. 8 minus 3, 0 minus 1, 0 minus 7, 8 minus 5. This is equal to 2 by 2 matrix in which elements are 5 minus 1 minus 7, 3. So 8A inverse is equal to this matrix. This implies A inverse is equal to 1 by 8 into this matrix. Hence our required answer is 1 by 8 into 2 by 2 matrix in which elements are 5 minus 1 minus 7, 3. So this completes the session. I am take care.