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Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det ≠ 0
Determinant of a 3x3 matrix is calculated by:
det
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.