The Tuareg people (despite being predominantly Muslims) have a culture where men veil their faces, while women do not

[u/medievalpeasant_]

[u/Lukainka]

It's matrilinear, not matriarchal. It's a patriarchal society with matrilinear kinship.

Edit: for more depth see comment below from u/AdAlternative7148

To describe Tuareg social organization as “matriarchal” is to conflate matrilineal descent reckoning with the institutional distribution of gendered authority. A more analytically defensible formulation would characterize it as a predominantly androcentric sociopolitical regime embedded within a matrilineally articulated kinship structure, wherein descent, filiative identity, property transmission, and certain successionary prerogatives are mediated through the uterine line without thereby constituting a generalized inversion of patriarchal power relations.

[u/AdAlternative7148 → u/Lukainka]

To describe Tuareg social organization as “matriarchal” is to conflate matrilineal descent reckoning with the institutional distribution of gendered authority. A more analytically defensible formulation would characterize it as a predominantly androcentric sociopolitical regime embedded within a matrilineally articulated kinship structure, wherein descent, filiative identity, property transmission, and certain successionary prerogatives are mediated through the uterine line without thereby constituting a generalized inversion of patriarchal power relations.

[u/Datpanda1999 → u/AdAlternative7148]

So in other words…it’s a patriarchal society with matrilinear kinship.

[u/notsocoolnow → u/Datpanda1999]

Not precisely. The inheritance is bifurcated, so his comment is accurate.

[u/Datpanda1999 → u/notsocoolnow]

Even if that’s the case (and I’ll assume it is as I’m not familiar with the specifics of their culture), from my understanding it’s not uncommon for a matrilineal society to have some form of matrilineal inheritance even if the society is overall patriarchal