B.R.A.I.N. is a robot of The Brain from the Animaniacs reboot who was built to help take over the world. He ends up being the main Antagonist of "Ex-Mousina".
Being a robot of The Brain built by The Brain, B.R.A.I.N. looks like a robotic version of him with a unicycle to move around.
Realizing how capable artificial intelligence is, Brain decides to build a robot of himself to aid him in taking over the world. Upon introducing B.R.A.I.N. to Pinky, the Brain decides to spend some time bonding with his new creation.
After spending some time, he presents his plan to B.R.A.I.N. only for it to be scoffed at before B.R.A.I.N. presents his own plan and revealing himself to have become even smarter than the Brain, much to Brain's dismay. Upon which, B.R.A.I.N. deducts that the only way he can progress with taking over the world is to destroy his creator along with Pinky.
Before he can though, Pinky asks him a question he had asked Brain at the beginning of the episode that causes B.R.A.I.N. to short circuit on account of the question being the equivalent of dividing by zero.