Can I have a step-by-step explanation for the following question?

Question

Can I have a step-by-step explanation for the following question?

Let {v_1, v_2,....., v_n} be a basis for a vector space V .

(a) Let T : V --> W be a linear transformation.

Prove that if T(v_1) = T(v_2) = ... = T(v_n) = 0, then T is the zero transformation.

(b) Let T : V --> V be a linear transformation.

Prove that if, T(v_1) = v_1, T(v_2) = v_2 ....T(v_n) = v_n, then T is the identity transformation on V .

Answer 1

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