give an example of a linear transformation $\displaystyle \, T:R^2 \rightarrow R^2$ where $\displaystyle T^2=T$ and $\displaystyle 0,1$ are the eigenvalues.

Attempt:

$\displaystyle

T(x,y) = (x,0)$

$\displaystyle *T(T(x,y) = T(x,0) = (x,0)$

$\displaystyle *T(x,y) = (x,0)$

$\displaystyle T(1,0) = (1,0) = 1(1,0)$

$\displaystyle T(0,1) = (0,0) = 0(0,1)$

Is this correct?

Thanks!