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Question Number 32499 by 7991 last updated on 26/Mar/18

proof: a(−b)=(−a)b=−(ab)

proof:a(−b)=(−a)b=−(ab)

Answered by $@ty@m last updated on 26/Mar/18

We have: 3×2=6 3×1=3 3×0=0 if we continue the process, the no. next to 2,1,0 would be −1 & no. next to 6,3,0 would be −3 Hence 3×(−1)=−3 ⇒a(−b)=−ab

Wehave:3×2=63×1=33×0=0ifwecontinuetheprocess,theno.nextto2,1,0wouldbe−1&no.nextto6,3,0wouldbe−3Hence3×(−1)=−3⇒a(−b)=−ab

Answered by Joel578 last updated on 26/Mar/18

We know for a, b ∈ R (−1) . a = −a and (−1) . b = −b a(−b) = a . [(−1)b] = [a(−1)] . b = (−a)b a(−b) = a . [(−1)b] = (−1) . (ab) = −ab (−a)b = [(−1)a]. b = (−1) . (ab) = −ab

Weknowfora,b∈R(−1).a=−aand(−1).b=−ba(−b)=a.[(−1)b]=[a(−1)].b=(−a)ba(−b)=a.[(−1)b]=(−1).(ab)=−ab(−a)b=[(−1)a].b=(−1).(ab)=−ab

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