Recovering unknown entries from a matrix square

A $3\times3$ matrix $A$ has rows $(1,x,-1)$, $(2,-2,y)$ and $(0,3,0)$, where $x$ and $y$ are unknown. You are told that $A^2$ has rows $(9,-7,11)$, $(-2,21,-8)$ and $(6,-6,9)$. What is the product $xy$?

$12$. The $(1,1)$ entry of $A^2$ is $1+2x=9$, so $x=4$. The $(2,2)$ entry is $2x+4+3y=21$, so $y=3$, and all other entries check out with $x=4$, $y=3$.