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Let $$A$$ be a $$n \times n$$ matrix such that $$|A| = 2$$. If the determinant of the matrix $$\text{Adj}\left(2 \cdot \text{Adj}(2A^{-1})\right)$$ is $$2^{84}$$, then $$n$$ is equal to ______.
Correct Answer: 2
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