Atlantis could have been been matrilineal and matriarchical

According to Atlantis Quest – Uncovering the Secrets that Prove Plato Right, both Native American tribes who live on the West side of the Atlantic Ocean and the Basques who live on the East side of the Atlantic Ocean share the same mitochondrial DNA haplogroup X–giving rise to speculation that they both spring from a common ancestor who lived on a landmass in the Atlantic Ocean, the lost continent of Atlantis.

Interestingly, many Native Americans tribes are often matrilineal (inheritance and descent spring from the female line) and matriarchal (ruled by women).

Could the Native Americans derive their rulership and inheritance traditions from the same place their derived their mitochondrial DNA haplogroup X?