# Reference request: arranging distinct numbers into a full rank matrix

I thought of the following problem:

Let $$n\ge 2$$. Suppose you have $$n^2$$ distinct numbers in some field. Is it necessarily possible to arrange the numbers into an $$n\times n$$ matrix of full rank (ie, nonsingular or invertible)?

(I am able to solve the problem, for example using the combinatorial nullstellensatz.)

I was wondering whether this problem was previous stated elsewhere, perhaps even on this site?

My original motivation for the problem was in fact quite similar to this question, but I was rearranging the primes.

• Do you have an answer for the field of Reals? Nov 7, 2018 at 10:56
• @dmtri: It's possible, for all fields. Nov 9, 2018 at 0:54