Question: 4. Let V be a nite-dimensional vector spaces and T: V } v a linear map. If there exists S: V > V such that

4. Let V be a nite-dimensional vector spaces and T: V } v a linear map. If there exists S: V > V such that T3 = I, prove that T is injective. Show that this fails if V is allowed to be innite- dimensional . [4]

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