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 ________.

Let $$A$$ be a $$3 \times 3$$ matrix of non-negative real elements such that $$A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$$. Then the maximum value of $$\operatorname{det}(\mathrm{A})$$ is _________.

Let A be a $$3 \times 3$$ matrix and $$\operatorname{det}(A)=2$$. If $$n=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots . .(\operatorname{adj} A))}_{2024-\text { times }}))$$, then the remainder when $$n$$ is divided by 9 is equal to __________.