Mathematics - Hyperbola Question with Solution | TestHub

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 $\text{ length of semi major axis is }x\text{ and semi minor axis is }y$, eccentricity is $\mathrm{e}$ and the length of the latus rectum is $l$, then $81\left(e^4+l^2\right)$ is equal to