We have to prove that if a + b = 0, then b = -a

a + b = 0

add -a to both the sides, this can be done for any values of a and b

=> a + b - a = 0 - a

=> b =...

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We have to prove that if a + b = 0, then b = -a

a + b = 0

add -a to both the sides, this can be done for any values of a and b

=> a + b - a = 0 - a

=> b = -a

**This proves that if a + b = 0, b = -a or that the additive inverse of a number is unique.**