Step 1: Understanding Sankhyakarika.
Sankhyakarika is the foundational text of Sankhya Philosophy, one of the six classical systems of Indian philosophy. It systematically presents the dualistic doctrine of Purusha (consciousness) and Prakriti (matter).
Step 2: Authorship.
The Sankhyakarika was written by Ishwarakrishna, a philosopher of the 4th century CE. His work preserved and summarized the earlier oral teachings of Kapila, who is traditionally considered the founder of Sankhya Philosophy.
Step 3: Elimination of wrong options.
- Option (1) Shrikrishnah: Not related to Sankhyakarika authorship.
- Option (2) Krishnadvaipayanah: This is Ved Vyasa, compiler of the Mahabharata, not the author here.
- Option (3) Murarikrishnah: No philosophical text attributed to him in this context.
- Option (4) Ishwarakrishnah: Correct, author of Sankhyakarika.
Step 4: Conclusion.
Thus, Ishwarakrishna is the author of Sankhyakarika.