Can someone help me how to proceed with this question?
An arrangement is made of $n^2$ scalars from $\Bbb{F}$ (a finite field) in $n$ rows and $n$ columns such that each row and column can be viewed as a vector in $\Bbb{F}^n$. Suppose $\Bbb{F}$ has $p$ elements. Then find the number of distinct arrangements such that all columns are linearly independent.
Update: So according to hint by @N.S. I find the answer will be $$\prod_{i=0}^{n-1}(p^n-p^i)$$ Am I right?
Hint
The first row can be any vector in $\mathbb F^n$, excepting $(0,0,..,0)$. You have $p^n-1$ choices for the first row.
The second row can be any vector excepting a scalar multiple of the first row. How many choices do you have?
The third row can be any vector excepting a linear combination of the first two rows. As there are two scalars to chose, how many choices do you have?
And so on, you can figure out one by one how many choices you have for each row.
