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.

  • $\begingroup$ Do you have an answer for the field of Reals? $\endgroup$
    – dmtri
    Nov 7, 2018 at 10:56
  • 1
    $\begingroup$ @dmtri: It's possible, for all fields. $\endgroup$
    – A. Rex
    Nov 9, 2018 at 0:54


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