The reaction proceeds as follows:
\[2\text{Fe}^{3+} + 2\text{I}^- \rightarrow 2\text{Fe}^{2+} + \text{I}_2\]
\[2\text{Fe}^{2+} + \text{S}_2\text{O}_8^{2-} \rightarrow 2\text{Fe}^{3+} + 2\text{SO}_4^{2-}\]
In this reaction:
Fe$^{3+}$ oxidizes I$^-$ to I$_2$ and converts itself to Fe$^{2+}$.
Fe$^{2+}$ reduces S$_2$O$_8^{2-}$ to SO$_4^{2-}$ and converts itself back to Fe$^{3+}$
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to: