Step 1: Understand the historical context.
The Poona Pact was an important political agreement signed during the Indian freedom struggle. In 1932, the British Government announced the Communal Award, which provided separate electorates for the Depressed Classes (Scheduled Castes). Mahatma Gandhi strongly opposed this provision because he believed it would divide Hindu society permanently.
Step 2: Mahatma Gandhi's protest.
To oppose the provision of separate electorates, Mahatma Gandhi began a fast unto death while imprisoned in Yerwada Jail, Pune. His fast created widespread concern throughout the country and increased pressure on national leaders to reach a compromise.
Step 3: Role of Dr. B.R. Ambedkar.
Dr. Bhimrao Ramji Ambedkar was the principal leader representing the Depressed Classes. He believed that separate electorates would ensure proper political representation for the oppressed communities. However, considering the national situation and Gandhi's fast, he entered into negotiations with Gandhi to find a mutually acceptable solution.
Step 4: Signing of the Poona Pact.
After several rounds of discussion, Mahatma Gandhi and Dr. B.R. Ambedkar signed the Poona Pact on 24 September 1932. According to the agreement, the provision of separate electorates was withdrawn, but the number of reserved seats for the Depressed Classes in provincial legislatures was increased. Thus, the Pact ensured greater political representation while maintaining a joint electorate system.
Step 5: Eliminate the incorrect options.
Jawaharlal Nehru was not a party to the Poona Pact, so Option (B) is incorrect. Lord Irwin was associated with the Gandhi-Irwin Pact (1931), not the Poona Pact, making Option (C) incorrect. M.A. Jinnah also did not sign the Poona Pact, so Option (D) is incorrect. Therefore, only Option (A) is correct.
Step 6: Final conclusion.
The Poona Pact was signed between Dr. Bhimrao Ambedkar and Mahatma Gandhi in 1932. Hence, the correct answer is:
\[
\boxed{\textbf{(A) Bhimrao Ambedkar and Mahatma Gandhi}}
\]