Exercise 1B Problem 1

Linear Algebra Done Right - Exercise 1B Problem 1 - Solution

June 12, 2022 · 1 min · 40 words · Me | Suggest Changes

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Problem

Prove that $-(-v) = v$ for every $v \in V$

Solution

By direct computation: $$-(-v) \stackrel{T1.31}{=} (-1)(-v) \stackrel{T1.31}{=} (-1)\left((-1)v\right) \stackrel{P1A13}{=} \left((-1)(-1)\right)v = 1v \stackrel{D1.19}{=} v$$ Proving that the additive inverse of an additive inverse of $v$ is $v$ itself.

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