Matrices and Determinants: JEE Main 2024 Mathematics question

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 $\mathrm{A}^2+x \mathrm{~A}+y \mathrm{I}=\mathrm{O}$ lie on a hyperbola, whose transverse axis is parallel to the $x$-axis, eccentricity is $\mathrm{e}$ and the length of the latus rectum is $l$, then $\mathrm{e}^4+l^4$ is equal to ________.