Step 1: Understanding the Question:
The question asks to identify the author of the ancient Sanskrit grammatical text known as "Ashtadhyayi".
Step 2: Key Formula or Approach:
This is a knowledge-based question. The approach is to recall or identify the correct author from the field of ancient Indian literature and scholarship and eliminate the incorrect options based on their known works.
Step 3: Detailed Explanation:
"Ashtadhyayi", meaning "eight chapters", is the foundational text of Sanskrit grammar. It was authored by the ancient Indian grammarian Panini. His work is considered a masterpiece of brevity and completeness, laying down the rules for classical Sanskrit.
Let's review the other options:
(A) Kalidasa: A famous classical Sanskrit poet and dramatist, known for works like "Abhijnanashakuntalam" and "Meghaduta".
(C) Chanakya (also known as Kautilya): An ancient Indian philosopher and royal advisor, famous for the political treatise "Arthashastra".
(D) Patanjali: An ancient sage who authored the "Mahabhashya", a detailed commentary on Panini's "Ashtadhyayi", and is also associated with the Yoga Sutras.
Step 4: Final Answer:
The author of "Ashtadhyayi" is Panini. Therefore, option (B) is correct.