JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A\) is a \(3 \times 3\) matrix and \(| A |=2\), then \(\left|3 \operatorname{adj}\left(|3 A| A^2\right)\right|\) is equal to \(.........\).
- A \(3^{11} \cdot 6^{10}\)
- B \(3^{12} \cdot 6^{10}\)
- C \(3^{10} \cdot 6^{11}\)
- D \(3^{12} \cdot 6^{11}\)
Answer & Solution
Correct Answer
(A) \(3^{11} \cdot 6^{10}\)
Step-by-step Solution
Detailed explanation
\(\left|3 \operatorname{adj}\left(|3 A| A^2\right)\right|=3^3\left|\operatorname{adj}\left(54 A^2\right)\right|=3^3 \cdot\left|54 A^2\right|^2\) \(=3^3 \times 54^0 \times|A|^4=3^{11} \times 6^{10}\)
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