Mathegoras

Vectors and matrices › Matrices › Inverses and singular matrices

Quadruples matching a matrix inverse identity

High school · ●●○○○ 20 pts

Find the number of ordered quadruples (a,b,c,d)(a,b,c,d) of real numbers such that (abcd)−1=(1a1b1c1d)\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}.

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