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Matrices and Determinants question

2024 · 9 Apr · Shift 1 · Q59

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JEE Main
Mathematics
Matrices and Determinants
2024 · 9 Apr · Shift 1 · Q59

Matrices and Determinants question

2024 · 9 Apr · Shift 1 · Q59

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1

Let

A

be a non-singular matrix of order 3. If

\operatorname{det}(3 \operatorname{adj}(2 \operatorname{adj}((\operatorname{det} A) A)))=3^{-13} \cdot 2^{-10}

and

\operatorname{det}(3\operatorname{adj}(2 \mathrm{A}))=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}

, then

|3 \mathrm{~m}+2 \mathrm{n}|

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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