\textbf{138-} Matrix $A = \begin{bmatrix} 1 & -\sqrt{3} \\ \sqrt{3} & 1 \end{bmatrix}$ is given. If matrix $A^2$ acts on point $(1, 2, -2)$, what are the coordinates of the resulting point?
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(1) $(-16, 8)$ \hfill (2) $(-8, 16)$ \hfill (3) $(8, -16)$ \hfill (4) $(16, -8)$
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