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Let \(a \in \mathbb{R}\). Show that the \(3 \times 3\) system \(\{a x + y + z = 1 \;;\; x + a y + z = 1 \;;\; x + y + a z = 1\}\) has a unique solution if and only if \(a \notin \{1, -2\}\), and identify the unique solution in that case.
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