JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) matrix and \(\operatorname{det}(A)=2\). If \({n}=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots (\operatorname{adj} A)}_{2024\ -\text { times }})))\). Then the remainder when \(\mathrm{n}\) is divided by \(9\) is equal to
- A \(7\)
- B \(9\)
- C \(10\)
- D \(11\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\(|\mathrm{A}|=2 \) \(\underbrace{\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \ldots . .(\mathrm{a})))}_{2024 \text { times }}=|\mathrm{A}|^{(\mathrm{n}-1)^{2024}} \) \( \quad=|\mathrm{A}|^{2024} \) \( =2^{2^{2024}}\)…
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