JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a square matrix of order 3 such that \(\operatorname{det}(A)=-2\) and \(\operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=2^{\mathrm{m}+\mathrm{n}} \cdot 3^{\mathrm{mn}}, \mathrm{m}\gt\mathrm{n}\). Then \(4 \mathrm{~m}+2 \mathrm{n}\) is equal to _______
- A 30
- B 32
- C 36
- D 34
Answer & Solution
Correct Answer
(D) 34
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { As } A \operatorname{adj} A=|A| l, \operatorname{det}(\lambda A)=\lambda^n \operatorname{det} A \\ & \operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=3^3 \operatorname{det}(\operatorname{adj}(-6 \operatorname{adj}(3 A))) \\ & =3^3(-6…
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