Question: Let V be a finite dimensional vector space, and T : V - V a linear transformation. (a) If T2 = T, show that N(T)

Let V be a finite dimensional vector space, and T : V - V a linear transformation. (a) If T2 = T, show that N(T) OR(T) = V [Hint: use dimension theorem (b) If 72 = 1, then determine N(T) and R(T). Does the same property from (a) holds true? ( c) Now assume V is infinite dimensional. Do the statements in (a) and (b) still hold true? Justify your

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