Q. Let $A = ⎣ ⎡ β γ - α^{2} γ α - β^{2} α β - γ^{2} γ α - β^{2} α β - γ^{2} β γ - α^{2} α β - γ^{2} β γ - α^{2} γ α - β^{2} ⎦ ⎤$ where $α, β, γ$ are roots of the equation $x^{3} - 2 x^{2} + 2 x - 3 = 0$ Now, consider $f (x) = ∣ A - x I ∣$ , where $I$ is identity matrix of order 3 .
The sum of the roots of the equation $f (x) = 0$ , is-

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Solution: