JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a matrix of order \(3 \times 3\) and \(|A|=5\). If \(|2 \operatorname{adj}(3 \mathrm{~A} \operatorname{adj}(2 \mathrm{~A}))|=2^\alpha \cdot 3^\beta \cdot 5^\gamma \alpha, \beta, \gamma \in \mathrm{N}\) then \(\alpha+\beta+\gamma\) is equal to
- A \(25\)
- B \(26\)
- C \(27\)
- D \(28\)
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & |2 \operatorname{adj}(3 \mathrm{~A} \operatorname{adj}(2 \mathrm{~A}))| \\ & 2^3 \cdot|3 \mathrm{~A} \operatorname{adj}(2 \mathrm{~A})|^2 \\ & 2^3 \cdot\left(3^3\right)^2 \cdot|\mathrm{~A}|^2 \cdot|\operatorname{adj}(2 \mathrm{~A})|^2 \\ & 2^3 \cdot 3^6…
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