JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \( |A|=6 \) where A is a \( 3 \times 3 \) matrix. If \( |adj(3adj(A^{2} \cdot adj(2A)))|=2^{m} \cdot 3^{n} \), \( m, n \in N \), then \( m+n \) is equal to:
- A 60
- B 62
- C 64
- D 66
Answer & Solution
Correct Answer
(B) 62
Step-by-step Solution
Detailed explanation
\(\operatorname{adj} 2 A=2^2 \operatorname{adj} A \quad \because \operatorname{adj} kA = k ^{ n -1}(\operatorname{adj} A)\) \(=4 \operatorname{adj} A\) Now \(A ^2(\operatorname{adj} 2 A)=4 A(\operatorname{adj} A )\) \(=4 A| A | I _3\) \(=24 A\) Now…
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