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Question 70

Let $$B = \begin{bmatrix} 1 & 3 \\ 1 & 5 \end{bmatrix}$$ and $$A$$ be a $$2 \times 2$$ matrix such that $$AB^{-1} = A^{-1}$$. If $$BCB^{-1} = A$$ and $$C^4 + \alpha C^2 + \beta I = O$$, then $$2\beta - \alpha$$ is equal to

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