Final answer:
The first Jamatkhana was established in Alamut, Iran. This place served as a central institution for the Ismaili community during its flourishing period in the region.
Step-by-step explanation:
The first Jamatkhana, a place of gathering for prayer and communal activities in Ismaili Islam, was not established in Cairo, Kabul, or Multan, but instead historians and records suggest that the earliest Jamatkhana was established in Alamut, Iran, under the Nizari Ismaili state during the time when the Ismaili community was flourishing in that region. The Alamut period was marked by the establishment of a state and community life where the Jamatkhana would have played a central role for the Ismaili believers.
The term 'Jamatkhana' itself is derived from the Arabic words 'jama'ah' meaning gathering and 'khana' meaning house or place, effectively translating to a 'gathering place'. Within the historical context of the Ismaili community, the Jamatkhana serves as a pivotal institution, which is evident from its early roots in Alamut, a place that holds significance within the Ismaili history.