\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(\mathcal{B} = \bigl((-1, 1, 1), (1, -1, 1), (1, 1, -1)\bigr)\) is a basis of \(\mathbb{R}^3\).
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