\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(a, b \in \mathbb{R}\). Find a condition on \((a, b)\) for \(\mathcal{F} = \bigl((1, a), (b, 1)\bigr)\) to be a basis of \(\mathbb{R}^2\).
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