Answer
See solution below
Work Step by Step
If T is an invertible linear transformation, there exists a linear transformation $S: R^n \to R^n$ such that $S(T(x))=x$ and $T(S(x))=x$ for all x in $R^n$.
Consider u and v in $R^n$ such that $x=S(u)$ and $y=S(v)$. Then, $T(x)=T(S(u))=u$ and $T(y)=T(S(v))=v$.
$T(x+y)=T(x)+T(y)$
$S(T(x+y))=x+y=S(T(x)+S(T(y))S(T(x)+T(y))$
$T(cx)=cT(x)$
$S(T(cx))=cx=cS(T(x))=S(cT(x))$
