JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]\) and \(A\) be a \(2 \times 2\) matrix such that \(\mathrm{AB}^{-1}=\mathrm{A}^{-1}\). If \(\mathrm{BCB}^{-1}=\mathrm{A}\) and \(\mathrm{C}^4+\alpha \mathrm{C}^2+\beta \mathrm{I}=\mathrm{O}\), then \(2 \beta-\alpha\) is equal to :
- A \(16\)
- B \(2\)
- C \(8\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
\( \mathrm{BCB}^{-1}=\mathrm{A} \) \( \Rightarrow\left(\mathrm{BCB}^{-1}\right)\left(\mathrm{BCB}^{-1}\right)=\mathrm{A} \cdot \mathrm{A} \) \( \Rightarrow \mathrm{BCI} \mathrm{CB^{-1 } = \mathrm { A } ^ { 2 }} \) \( \Rightarrow \mathrm{BC}^2 \mathrm{~B}^{-1}=\mathrm{A}^2 \)…
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