Determine a linear transformation T:V2->V2 , which maps all the vectors on the line x+y = 0 onto thmeselves (T is not I).
$\displaystyle x+y=0\Longleftrightarrow y=-x\Longleftrightarrow $ the vector $\displaystyle (1,-1)$ , generator of the above line, must be mapped either to himself or to another vector in the same line, so you can try $\displaystyle T(x,y):=(y,x)$ . Now check T is a lin. trans. and it maps the above line to itself.
Tonio