JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) matrix such that \(|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4\). Then \(\left| A ^{-1} \operatorname{adj} A \right|\) is equal to
- A \(2 \sqrt{3}\)
- B \(\sqrt{6}\)
- C \(12\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Given \(|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} . A ))|=12^4\) \(\Rightarrow| A |^{(n-1)^3}=12^4\) Given \(n =3\) \(\Rightarrow| A |^8=12^4\) \(\Rightarrow| A |^2=12\) \(| A |=2 \sqrt{3}\) We are asked \(\left| A ^{-1} \cdot \operatorname{adj} A \right|\)…
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