If A is a square matrix of order 3 such that det(A)=3 and det(adj(-4 adj(-3 adj(3 adj((2 ~A)⁻¹)))))=2^(m) 3ⁿ, then m+2 n is equal to:

Matrices and Determinants: JEE Main 2024 Mathematics question

JEE Main 2024 · 6 Apr, Evening shift · Q4431

JEE Main 20246 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

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 :

JEE Main 2024 · 6 Apr, Evening shift · Q4431

JEE Main 20246 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

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 :