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I hope you guys help me with this exercise in the book "Linear Algebra Done Right"

## Homework Statement

" Give an example of a nonempty subset ##U## of ##R^2## such that ##U## is closed under addition and under taking additive inverses (meaning ##−u## ##∈## ##U## whenever ##u## ##∈## ##U##), but ##U## is not a subspace of ##R^2##."

## Homework Equations

3. The Attempt at a Solution [/B]

From what I understood from the question, the subset must not be closed under multiplication because it is closed under addition as well as the additive inverses which imply that ##0## vector must exist.

So the only thing that would make it non-subspace is the multiplication.

Hope you guys correct my understanding and help me with the solution.