In the Reimer-Tiemann reaction, phenol reacts with chloroform (CHCl$_3$) and aqueous sodium hydroxide (NaOH) to form salicylaldehyde via the following mechanism:
Phenol undergoes ortho-substitution due to the electrophilic attack of dichlorocarbene (:CCl$_2$), generated in situ from CHCl$_3$ and NaOH.
The intermediate formed is the sodium salt of dichlorophenol.
On further hydrolysis and protonation, salicylaldehyde is obtained.
The reaction proceeds as:
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: