3 years, 3 months ago
How do you prove -1*x=-x using arithmetic axioms?
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M$1 Answer
the multiplicative identity property states that for any real number a, 1 × a = a.
(a × (-1)) + (a × 1) = a × (1 + (-1))
(a × (-1)) + (a × 1) = a × 0
(a × (-1)) + (a × 1) = 0
a × (-1) = -(a × 1)
a × (-1) = -a
(a × (-1)) + (a × 1) = a × (1 + (-1))
(a × (-1)) + (a × 1) = a × 0
(a × (-1)) + (a × 1) = 0
a × (-1) = -(a × 1)
a × (-1) = -a
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