-1

I want to calculate the size of $GL_n(\mathbb{F}_p)$.

Originally I was locking specifically for the size of $GL_2(\mathbb{F}_5)$ but I managed to calculate it by directly calculating ${\{A\in M_2(\mathbb{F}_5)\mid detA=0\}}$ and some arithmetic. I was wondering if there is a generalization and couldn't find one.

Thanks in advance!

asdasdasda
  • 51
  • 1
    $p^n-1$ choices for the first row, then the $k+1$-th row must be taken outside of the vector subspace generated by the $k$ previous rows, so $p^n-p^k$ choices. – reuns Apr 20 '21 at 00:17

1 Answers1

0

This question has been asked many times.

Developing the hint in the comments, we get $\prod_{k=0}^{n-1}(p^n-p^k) $.