Let A be a square matrix of order 2 such that | A |=2 and the sum of its diagonal elements is -3. If the points (x, y) satisfying A^2+x A +y I = O…

Let A be a square matrix of order $\displaystyle 2$ such that $\displaystyle |\mathrm{A}|=2$ and the sum of its diagonal elements is -$\displaystyle 3$ . If the points $\displaystyle (x, y)$ satisfying $\displaystyle \mathrm{A}^2+x \mathrm{~A}+y \mathrm{I}=\mathrm{O}$ lie on a hyperbola, whose transverse axis is parallel to the $\displaystyle x$-axis, eccentricity is $\displaystyle e$ and the length of the latus rectum is $\displaystyle l$, then $\displaystyle e^4+l^4$ is equal to $\displaystyle \_\_\_\_$.