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When doubly-affine matrices such as Latin and magic squares with a singlenon-zero eigenvalue are powered up they become constant matrices after a fewsteps. The process of compounding squares of orders m and n can then be used togenerate an infinite series of such squares of orders mn. The Cayley-Hamiltontheorem is used to understand this property, where their characteristicpolynomials have just two terms.

Powers of doubly-affine integer square matrices with one non-zero eigenvalue