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Self-inverse 2x2 matrices

High school · ●●○○○ 20 pts

The matrix (a3−8d)\begin{pmatrix} a & 3 \\ -8 & d \end{pmatrix} is its own inverse, for some real numbers aa and dd. Find the number of possible pairs (a,d)(a,d).

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matrix inverse2x2 matricessystems of equations