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Milica
Milica asked in Science & MathematicsMathematics · 9 years ago

Prove that for all a,b in a ring R, (−a)b = −(ab) = a(−b)?

A really need help for this, my hw due in soon..

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  • Suleiman
    Lv 6
    9 years ago
    Favorite Answer

    0 = 0⋅b = ((-a) + a)⋅b = (-a)b + ab

    ⇒ -(ab) = 0 + (-(ab)) = ((-a)b + ab) + (-(ab)) = (-a)b + (ab + (-(ab))) = (-a)b + 0 = (-a)b

    (Proof that -(ab) = a(-b) is similar).

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