\textbf{139-} If matrix $A$ has the transformation $T(x,y) = (2x - y,\ 3x - 4y)$ and $I$ is the identity matrix, and $\alpha$ and $\beta$ are two real numbers such that $\alpha A + \beta I = A^{-1}$, what is the value of $\beta$?
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(1) $-\dfrac{3}{5}$ \hfill (2) $-\dfrac{1}{5}$ \hfill (3) $\dfrac{2}{5}$ \hfill (4) $\dfrac{4}{5}$
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