About Matrix Matrix is an open protocol for decentralised, secure communications.
Matrix Manifesto We believe:
People should have full control over their own communication. People should not be locked into centralised communication silos, but instead be free to pick who they choose to host their communication without limiting who they can reach. The ability to converse securely and privately is a basic human right. Communication should be available to everyone as a free and open, unencumbered, standard and global network.
https://fediverse.info/
To explain more specifically. Matrix is federated, so you can talk to other matrix servers like Lemmy instances can. However, matrix not part of the Fediverse, which is built on activity pub, which lets Lemmy, Masotodon, Pixfed and others all talk to each other.
Lemmy and Mastodon technically communicate on the same protocol, but they don’t currently communicate with each other in any meaningful way. Possibly in the future, but probably not imo.
I think you can comment on lemmy posts from a mastodon instance
Support for groups (i.e. communities on Lemmy) is coming to Mastodon sometime soon.