JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(n \times n\) matrix such that \(| A |=2\). If the determinant of the matrix \(\operatorname{Adj}\left(2 . \operatorname{Adj}\left(2 A ^{-1}\right)\right.\) ). is \(2^{84}\), then \(n\) is equal to \(................\)
- A \(10\)
- B \(12\)
- C \(16\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(\left|\operatorname{Adj}\left(2 Adj \left(2 A ^{-1}\right)\right)\right|\) \(=\left|2 \operatorname{Adj}\left(\operatorname{Adj}\left(2 A ^{-1}\right)\right)\right|^{ n -1}\) \(=2^{n(n-1)}\left|\operatorname{Adj}\left(2 A ^{-1}\right)\right|^{n-1}\)…
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