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1. Quadruples matching a matrix inverse identity ●●○○○ 20 ptsFind the number of ordered quadruples $(a,b,c,d)$ of real numbers such that $\begin{pmatrix} a & b \\ c & d \end{pmatrix}^{-1} = \begin{pmatrix} \frac{1}{a} & \frac{1}{b} \\ \frac{1}{c} & \frac{1}{d} \end{pmatrix}$.