Matrices And Determinants

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 ________.