The ethymology of matrix states it as meaning uterus, womb or pregnant animal.
Else please calm down. It is a service in testing, and as applicable to all other http://allmende.io services,
it is provided "as is", without warranty of any kind.
Therefore @gandhiano was only shooting to early in persuading users to join it.
To answer the questions:
Matrix is a distributed activity log which bridges multiple domains via so-called homeservers. Then it is up to the applications layered on top of it to give it a use.
It has been set up in trying to find alternatives to the commercial Slack communities, which have been spreading recently.
One examplanatory usage then is indeed a chat service with a glossy user facing component to give end users what they expect. It is a viable self-hosted alternative to Slack, gitter, Mattermost, Let's Chat, Scrollback.io, Rocket.Chat and the likes which provides ease of traversing domains and instances.
Chat rooms can be public, private, with or , without persistent logs, etc. Then integrations bridge into other networks.
Yes, there is rudimentary 1-on-1 support for audio and video conferencing. Keep in mind it is still in testing.
You can join rooms
If you ask me, yes. Should we escalate this question to Loomio et al.?