For matrix A= […] , the values of x and y so that A^2+xI=yA are :

The correct answer is Option (3) → $x=8, y = 8$

$A^2+xI=yA$

and,

$A=\begin{bmatrix}3&1\\7&5\end{bmatrix}$

$∴A^2+xI=\begin{bmatrix}16+x&8\\56&32+x\end{bmatrix}=y\begin{bmatrix}3&1\\7&5\end{bmatrix}$

$⇒(x,y)=(8,8)$