Question: Suppose T: V V is a linear operator with the property that T[T(v)] = v for all v in V. (For example, transposition in

Suppose T: V → V is a linear operator with the property that T[T(v)] = v for all v in V. (For example, transposition in Mnn or conjugation in C.) If v ≠ 0 in V, show that (v, T(v)) is linearly independent if and only if T(v) ≠ v and T(v) ≠ -v.

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