the set of linear transformations. Let S={T:$\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$:T is a linear
transformation with T(1,0,1)=(1,2,3), T(1,2,3)=(1,0,1)} .Then S is 
(a) A Singleton Set 
(b) A finite set containing more than one element
(c) A countable set
(d) An uncountable set
MY APPROACH: 
T(1,0,1)=(1,2,3)$\Longrightarrow$T(e$^{1}+e^{3})$=(e$^{1}+2e^{2}+3e^{3})$
$\Longrightarrow$T(e$^{1})$+ T(e$^{3})$=e$^{1}+2e^{2}+3e^{3}Similarly,$T(e$^{1})$+2T(e$^{2})$+3T(e$^{3})$=e$^{1}$+e$^{3}$
I cant think more than this

A geometrical way to look at it is take the midpoint of given input points as origin and consider any axis through that origin perpendicular to the line joining two points and revolve the space around that axis by 180 degrees. And you can make such uncountable infinite axes. So the set S Is uncountable set.
