## prove is a basis

Suppose that T, S $:R^n -->R^n$ are inverses, if { $v_1, v_2, ..., v_k$} is a basis for a subspace V of $R^n$and $w_1 = T(v_1), w_2 = T(v_2),....,w_k = T(v_k)$, prove that { $w_1, w_2,....w_k$} is a basis for T(V).
Give an example to show that this need not be true if T does not have an inverse.