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Let $$A$$ be a non-singular matrix of order 3. If $$\det(3 \text{ adj}(2 \text{ adj}((\det A)A))) = 3^{-13} \cdot 2^{-10}$$ and $$\det(3 \text{ adj}(2A)) = 2^m \cdot 3^n$$, then $$|3m + 2n|$$ is equal to ________
Correct Answer: 14
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