What is the size of a general linear group over a finite field?

In this video we compute the cardinality of the group of n-by-n invertible matrices over an arbitrary finite field. While this looks like a group-theoretic problem on the surface, the proof we give uses ideas mostly from linear algebra. In a future video, we will instead compute the cardinality of a special linear group over an arbitrary finite field. This proof will involve much more group theory, but this video should serve as a prerequisite. Feel free to suggest topics for future videos in the comments below.

[vaishnavikumar]

Please do make proof for all prerequisites