Here’s how to tell if you’re running Cinnamon or Mate.

<pre lang="bash">
inxi -Fxz

Result.

<pre lang="bash">
System: Kernel: 5.4.0-40-generic x86_64 
bits: 64 
compiler: gcc v: 9.3.0 
Desktop: Cinnamon 4.6.6 
Distro: Linux Mint 20 Ulyana 
base: Ubuntu 20.04 focal
...