JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\mathrm{A}\) be a \(3 \times 3\) real matrix. If \(\operatorname{det}(2 \operatorname{Adj}(2 \operatorname{Adj}(\operatorname{Adj}(2 \mathrm{~A}))))=2^{41}\), then the value of \(\operatorname{det}\left(A^{2}\right)\) equal ..... .
- A \(2\)
- B \(4\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(\operatorname{adj}\,(2 \mathrm{~A})=2^{2} \,\mathrm{adj} \mathrm{A}\) \(\Rightarrow \operatorname{adj}(\operatorname{adj}(2 \mathrm{~A}))=\operatorname{adj}(4 \mathrm{adj} \mathrm{A})=16 \mathrm{adj}(\operatorname{adj} \mathrm{A})\) \(=16\, |A|\,\mathrm{A}\)…
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