Solution
= Solution
There are $p^n$ choices for the translation. Choose the columns of an <invertible matrix> successively: the first is any nonzero column, the second avoids its span, and at stage $j+1$ one avoids a $j$-dimensional span of size $p^j$. Consequently
$$
\boxed{|G|=p^n\prod_{j=0}^{n-1}(p^n-p^j).}
$$
The successive <linear independence> conditions are exactly the criterion that the columns form a <basis>.