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gjm comments on Innate Mathematical Ability - LessWrong
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I think the proof is simplified by the observation that (+ meaning XOR) a+b=c is the same as a+b+c=0. So if all rows have the XOR property, we find that the XOR of all entries is 0. If two columns have the XOR property, the XOR of their entries is 0, leaving 0 for the XOR of the entries in the last column, and we're done.
Agreed; my proof doesn't make use of the fact that C⊕C=0, and if you use that fact you get there quicker.