Can we arrange $\{1,...,9\}$ in $3\times 3$ grid so the set of products of rows equals the set of products of columns?

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I find a interesting question of Prmo mock and Promys 2020

For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the set of products of rows?

I can find solution for $3\times 3$ or $4\times 4$ but unable to generalize for $n\times n$.

The question has been answered by RobPratt but I am not understanding his solution its too hard for me nor I can ask the doubt to him due to lower reputation

Can anyone please help me in this question.