NVAMediumJEE Main 2025 · 22 January, Shift 1Properties of Determinants

Mathematics Question from JEE Main 2025 · 22 January, Shift 1

Let AA be a square matrix of order 33 such that det(A)=2\det(A) = -2 and det(3adj(6adj(3A)))=2m+n3mn\det(3 \cdot \operatorname{adj}(-6 \cdot \operatorname{adj}(3A))) = 2^{m+n} \cdot 3^{mn}, where m>nm > n. Then 4m+2n4m + 2n is equal to:

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