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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be two \(3 \times 3\) matrices such that \(AB = I\) and \(| A |=\frac{1}{8}\) then \(|\operatorname{adj}( Badj (2 A ))|\) is equal to
- A \(16\)
- B \(32\)
- C \(64\)
- D \(128\)
Answer & Solution
Correct Answer
(C) \(64\)
Step-by-step Solution
Detailed explanation
\(AB = i\) \(\operatorname{ladj}\left( B\right.\) adj \((2 A )|=| B\) adj \(\left.(2 A )\right|^{2}\) \(\quad=| B |^{2}\) |adj \(\left.(2 A )\right|^{2}\) \(=| B |^{2}\left(|2 A |^{2}\right)^{2}=| B |^{2}\left(2^{6}| A |^{2}\right)^{2}\) \(| A |=\frac{1}{8}\) and…
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