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The problem was originally posed by Molnar in [molnar1974matrix].

Various authors followed up this article with both single solutions and parametric families of solutions:

Guy presents an overview and discusses variants of the problem [guy2004unsolved].

A CSP model is presented in [frisch2003constraints]

Richard Guy
Unsolved problems in number theory

Alan M Frisch, Chris Jefferson, and Ian Miguel
Constraints for breaking more row and column symmetries
Principles and Practice of Constraint Programming–CP 2003, 318–332, 2003

EA Molnar
A matrix problem
American Mathematical Monthly, 383–384, 1974