I think it's much more productive to teach children

    2x0 = 2x1 + 2x(-1) = 2-2 = 0

and

    2xx0 = 2xx1 x 2xx(-1) = 2/2 = 1

Inverting the concept and having those patterns stem from a fundamental identity can wait until its not seen as the mathematical equivalent of "Because I said so".