Step 1: Understanding the Concept:
The reaction sequence involves the functionalization of benzene into a Grignard reagent, followed by its reaction with a protic source (alcohol).
Step 2: Detailed Explanation:
1. Step 1 (\(Br_2/Fe/\Delta\)): This is electrophilic aromatic substitution (Bromination). Benzene reacts with bromine in the presence of an iron catalyst to form Bromobenzene (\(C_6H_5Br\)).
2. Step 2 (\(Mg/\text{dry ether}\)): The bromobenzene reacts with magnesium metal in dry ether to form the Grignard reagent, Phenylmagnesium bromide (\(C_6H_5MgBr\)).
3. Step 2 (\(CH_3OH\)): Grignard reagents are extremely strong bases and powerful nucleophiles. When they encounter a molecule with an acidic hydrogen (like the \(O-H\) hydrogen in methanol), they immediately undergo an acid-base reaction.
\[ C_6H_5MgBr + CH_3OH \rightarrow C_6H_6 + Mg(OCH_3)Br \]
The phenyl group picks up a proton to regenerate Benzene, and the magnesium forms a salt with the methoxide ion.
Step 3: Final Answer:
The final products are benzene and \(Mg(OCH_3)Br\), which corresponds to option (A).