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How -A multiplied by -B equals plus AB was determined and when?
Wiki User
∙ 10y ago
A*(B-B) = A*0 = 0
Expanding the left hand side, using the distributive property, A*B + A*(-B) = 0
That is, A*B and A*(-B) are additive inverses.
Next,
(A-A)*(-B) = 0*(-B) = 0
Expanding, A*(-B) + (-A)*(-B) = 0
Therefore A*(-B) and (-A)*(-B) are additive inverses
But, from above, the additive inverse of -A*B is A*B
Therefore (-A)*(-B) = A*B
It is not known when this was proven.
Wiki User
∙ 10y ago
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