Alpha Matrix

Algebra Level 3

\[ \begin{vmatrix} (1+\alpha)^{2} & (1+2\alpha)^{2} & (1+3\alpha)^{2} \\ (2+\alpha)^{2} & (2+2\alpha)^{2} & (2+3\alpha)^{2} \\ (3+\alpha)^{2} & (3+2\alpha)^{2} & (3+3\alpha)^{2} \end{vmatrix}= -648\alpha \]

From the set of values given in the options, select the value of \(\alpha\) that can satisfy the equation above.

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