If is a square root of the two-rowed unit matrix

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If [αβγ−α]\begin{bmatrix}\alpha&\beta\\\gamma&-\alpha\end{bmatrix} is a square root of the two-rowed unit matrix, then α\alpha, β\beta, and γ\gamma satisfy (1) 1−α2+βγ=01-\alpha^2+\beta\gamma=0 (2) α2+βγ−1=0\alpha^2+\beta\gamma-1=0 (3) 1+α2+βγ=01+\alpha^2+\beta\gamma=0 (4) 1−α2−βγ=01-\alpha^2-\beta\gamma=0

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