Step 1: Understanding the Concept:
This list covers prose writers, a modern novelist, a Champu writer, and a lyricist. Knowing their primary works is fundamental.
Step 3: Detailed Explanation:
1. Banabhatta: He is the greatest prose writer of the classical period.
His most famous work is the 'Katha' titled Kadambari.
Matching: A-III.
2. Ambikadatta Vyasa: He is a modern Sanskrit scholar (19th century).
He wrote the first modern historical Sanskrit novel titled Shivarajavijayam, depicting the life of Shivaji Maharaj.
Matching: B-I.
3. Trivikrama Bhatta: He is known for the first major Champu work.
His work Nalachampukavyam (or Damayanti-katha) is the earliest significant composition in the mixture of prose and poetry.
Matching: C-IV.
4. Bhartrihari: He is the famous author of the 'Shataka-traya'.
His Nitishatakam contains 100 verses on worldly wisdom and ethics.
Matching: D-II.
Resulting match: A-III, B-I, C-IV, D-II.
Step 4: Final Answer:
Matching authors to their masterpieces: A-III, B-I, C-IV, D-II. Thus, Option (A) is correct.