Step 1: Possessive Form Analysis. In the provided sentence, the subject "mother's" is singular, denoting possession by one mother. Therefore, the correct possessive form is indeed "mother's."
Step 2: Option Evaluation. - (A) My mother's official car is parked elsewhere: This option is correct due to the accurate use of the singular possessive "mother's." - (B) My mothers' official car is parked elsewhere: This option is incorrect. The possessive form "mothers'" implies multiple mothers, contradicting the singular context. - (C) My mother's official car is parked everywhere: While grammatically sound, this sentence deviates from the original meaning, which specifies the car's location as "elsewhere," not "everywhere." - (D) My mother's official cars is parked elsewhere: This option is incorrect. The plural noun "cars" creates a subject-verb agreement error with the singular subject "mother's."
Step 3: Determination. The correct choice is (A) My mother's official car is parked elsewhere. This sentence is both grammatically accurate and contextually appropriate.