Sylow $p$-Subgroups of $GL_n(\mathbb F_q)$

Question

I know that one of the Sylow $p$-subgrouops of $GL_n(\mathbb F_q)(q=p^a)$ is the subgroup $P$ of upper triangular matrices with $1$ on diagonal, but is there a simple and direct way to see that every Sylow $p$-subgroup is obtained by change of basis isomorphism $T^{-1}PT=\{T^{-1}UT: U\in P\}, T\in GL_n(\mathbb F_q)$ from this one(i.e. conjugate)? (This is Sylow's second theorem, but I'm seeking a more direct proof in this particular case. In fact, I also want to know if we can use this case to prove Sylow's second theorem by imbedding any group into $GL_n(\mathbb F_q)$?)