Originally Posted by

**aman_cc** Thanks very much. I'll try your hint to Q1.

Let T:V->V be a linear transformation. Am I correct in saying:

T is onto IFF T is one-one

Proof: Let v1,v2, v3...,vn be basis of V

T is onto => T(v1), T(v2), ... T(vn) span V hence is a basis of V. So if T(v) = 0 => v = 0. Which further => T is one-one

T is one-one. T(v1), T(v2)....T(vn) is basis for range of T which is a equal to/subspace of V. But any subspace of V with n basis = V itself hence T is onto.

Is my reasoning correct?