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mammarf
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Homework Statement
Prove that the additive inverse -v of an element v in a vector space is unique.
Homework Equations
Additive Inverse in V
For each v in V, there is an element -v in V such that v + (-v) = 0.
The Attempt at a Solution
Assume that the additive inverse is not unique and there exists different y,z in V such that
A + y = 0
A + z = 0
which implies y = -A and z = -A => y=z which is a contradiction.
Hence, the additive inverse is unique.
Correct? sumthin missing?