jee-main 2024 Q70

jee-main · India · session2_06apr_shift2 Matrices Determinant and Rank Computation
If $A$ is a square matrix of order 3 such that $\operatorname { det } ( A ) = 3$ and $\operatorname { det } \left( \operatorname { adj } \left( - 4 \operatorname { adj } \left( - 3 \operatorname { adj } \left( 3 \operatorname { adj } \left( ( 2 \mathrm {~A} ) ^ { - 1 } \right) \right) \right) \right) \right) = 2 ^ { \mathrm { m } } 3 ^ { \mathrm { n } }$, then $\mathrm { m } + 2 \mathrm { n }$ is equal to:
(1) 2
(2) 3
(3) 6
(4) 4
If $A$ is a square matrix of order 3 such that $\operatorname { det } ( A ) = 3$ and $\operatorname { det } \left( \operatorname { adj } \left( - 4 \operatorname { adj } \left( - 3 \operatorname { adj } \left( 3 \operatorname { adj } \left( ( 2 \mathrm {~A} ) ^ { - 1 } \right) \right) \right) \right) \right) = 2 ^ { \mathrm { m } } 3 ^ { \mathrm { n } }$, then $\mathrm { m } + 2 \mathrm { n }$ is equal to:\\
(1) 2\\
(2) 3\\
(3) 6\\
(4) 4