Matrix Representations of GF(p[superscript n]) over GF(p)

We show that any non-singular nxn matrix of order p[superscript n]-1 over GF(p) is a generator of a matrix representation of GF(p[superscript n]). We also determine the number of matrix representations of GF(p[superscript n])GF(p) over GF(p), and then number of order p[superscript n]-1 matrices in the general linear group of degree n over GF(p). The theorems are easily generalizable to arbitrary field extensions.