This problem is so famous. For first trivial reference, you can see:link.

$\it{Bodendiek}$ and $\it{Burosch}$ studied this problem in a paper with name:

"Solution to the Antimagic 0,1,-1 Matrix Problem."

Also, you can search about "Alternating sum matrix", for more information.

This problem is so famous. For first trivial reference, you can see:link.

$\it{R. Bodendiek}$ and $\it{G. Burosch}$ studied this problem in a paper with name:

"Solution to the Antimagic 0,1,-1 Matrix Problem."

If there is solution for integer $n$, then we have:

$1)$ $n$ is even,

$2)$ The number in $\{-n,1-n,2-n,...,n\}$ that does not appear as a line sum is either $-n$ or $n$,

$3)$ Of the $n$ largest line sums, half are column sums and half are row sums.

Also, you can search about "Alternating sum matrix", for more information.