A matrilineal society is one in which descent is traced through the female line. This often results in power and property descending down the female line as well. There are many examples of such societies.
The Merriam-Webster dictionary defines matrilineality as:
relating to, based on, or tracing descent through the maternal line
The Garos of India use a matrilineal clan system in which the youngest daughter typically inherits land from her mother. Men leave their paren't house at puberty and live in their wives house when they marry.
Another well known example are the Hopi of the United States which are also tradionally matrilocal. Like other examples they use a clan system. The women of the father's family will name children. The Hopi were also matrilocal and some researchers claim their society had a widespread belief in female superiority.
Jaintia was a kingdom in modern day Bangaldesh. The Jainta were known to be matrilineal. Tribes remaining in the area today, such as the Khasi and Garo are reported to be matrilineal. In both of these societies the youngest girl inherits the family property and unusually even among matrilineal societies daughters inhernit and run family businesses. Even among these tribes though, the monarchy was inherited by the son of the youngest daughter of the monarch. Both societies are also matrilocal.