let V be a real n-dimensional vector space and let T:V-->V be a LT saisfying T(v)= - v for all v belongs to V.
1. show n is even
Have you left something out? This statement does not follow from just what you have stated.
PS: I found your mistake. You want T[sup]2[/sup](v)= −v for all v ∈ V.
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