Solve a math puzzle involving matrices

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: [login to view URL] 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 freelancer.com NOTE(2): If you find the solution to this somewhere else, that is acceptable, just reference it and summarize the solution.