Step 1: Concept
Brihaddesi is one of the most significant post-classical Sanskrit treatises on Indian classical music, authored by Sage Matanga. It is estimated to have been compiled between the 6th and 8th centuries AD.
Step 2: Historical Importance
Matanga's Brihaddesi serves as a crucial bridge between the ancient Marga (liturgical/sacred) music and the Desi (secular/regional) classical music of India.
Step 3: Definition of Raga
Historically, this treatise is celebrated for providing the first-ever explicit definition of the word Raga: "Ranjayati iti Ragah" (that which pleases the mind of the listeners is a raga). It also introduced the early classification of ragas under Giti frameworks.
Step 4: Conclusion
Among the options provided, Matanga is the author of Brihaddesi, matching option (A).
Final Answer: (A)