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If \(\overline{\alpha \beta} \times \overline{\delta \beta} = \overline{\gamma \gamma \gamma}\), find the trace of the following matrix:

\[A = \huge{\left[ \begin{matrix} \alpha & 289 & 546 & 252 \\ 88 & \beta & 2573 & 245 \\ 758 & 353 & \gamma & 5725 \\ 100 & 212 & 35636 & \delta \end{matrix} \right] }\]

Details and assumptions

\(\alpha, \beta, \gamma\) and \(\delta\) are digits, eg \(\overline{\alpha \beta} \neq \alpha \times \beta\).

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