jee-main 2023 Q68

jee-main · India · session2_10apr_shift1 Matrices Determinant and Rank Computation

If $A$ is a $3 \times 3$ matrix and $|A| = 2$, then $|3\, \text{adj}(3A)| \cdot |A^2|$ is equal to
(1) $3^{12} \cdot 6^{11}$
(2) $3^{12} \cdot 6^{10}$
(3) $3^{10} \cdot 6^{11}$
(4) $3^{11} \cdot 6^{10}$

If $A$ is a $3 \times 3$ matrix and $|A| = 2$, then $|3\, \text{adj}(3A)| \cdot |A^2|$ is equal to\\
(1) $3^{12} \cdot 6^{11}$\\
(2) $3^{12} \cdot 6^{10}$\\
(3) $3^{10} \cdot 6^{11}$\\
(4) $3^{11} \cdot 6^{10}$

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