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Let $A = \begin{pmatrix} 0 & 2q & r \ p & q & -r \ p & -q & r \end{pmatrix}$. If $AA^T = I_3$, then $|p|$ is:
(1) $\dfrac{1}{\sqrt{5}}$
(2) $\dfrac{1}{\sqrt{3}}$
(3) $\dfrac{1}{\sqrt{2}}$
(4) $\dfrac{1}{\sqrt{6}}$
BETA
