JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\alpha \beta \neq 0\) and \(A=\left[\begin{array}{ccc}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]\). If \(B=\left[\begin{array}{ccc}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]\) is the matrix of cofactors of the elements of \(A\), then \(\operatorname{det}(A B)\) is equal to.
- A \(343\)
- B \(125\)
- C \(64\)
- D \(216\)
Answer & Solution
Correct Answer
(D) \(216\)
Step-by-step Solution
Detailed explanation
Equating co-factor fo \(\mathrm{A}_{21}\) \( \left(2 \alpha^2-3 \alpha\right)=\alpha \) \( \alpha=0,2 \text { (accept) }\) Now, \(2 \alpha^2-\alpha \beta=3 \alpha\) \( \alpha=2 \quad \beta=1 \) \( |A B|=|A \operatorname{cof}(A)|=|A|^3\)…
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