This is an experiment to see if freelancer can be combined with stackexchange to monetize problems.
I would like a solution to the following math puzzle:
[url removed, login to view]
If you can only solve the 2x2 or 3x3 cases, that is acceptable. If the solution is a proof that such a matrix construction does not exist, the proof steps must be written clearly and explicitly.
NOTE: Your work should be submitted via freelancer.com. Of course you are free to post your work on stackexchange as well, but the official work must be submitted as usual on [url removed, login to view]
NOTE(2): If you find the solution to this somewhere else, that is acceptable, just reference it and summarize the solution.