Why the restriction for u?

Algebra Level 4

\[\large A = \begin{vmatrix}u & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \\ \end{vmatrix} \]

If \(\det(adj(adj(A))) = 23^4 \), then what is the possible integral value of \(u \ ? \)

Note

  • \(u \neq -\dfrac{11}{3} \)

  • \(u \in \mathbb{R} \)


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