answersLogoWhite

0

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.

User Avatar

Wiki User

11y ago

What else can I help you with?