JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) invertible matrix. If \(|adj (24 A ) \mid=\) \(\operatorname{adj}(3 \operatorname{adj}(2 A )) \mid\), then \(\mid A ^{2}|=\dots\dots\dots\) is equal to
- A \(6^{6}\)
- B \(2^{12}\)
- C \(2^{6}\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(2^{6}\)
Step-by-step Solution
Detailed explanation
\(\operatorname{ladj}(24 A )|=\operatorname{ladj} 3(\operatorname{adj} 2 A )|\) \(\Rightarrow|24 a |^{2}=(3 \operatorname{adj}(2 A ))^{2}\) \(\Rightarrow\left(24^{3}| A |\right)^{2}=\left(3^{3} \operatorname{ladj}(2 A ) \mid\right)^{2}\) \(=3^{6}\left(\mid 2 Al ^{2}\right)^{2}\)…
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