Is it possible for a linear operator T: R^2-- R^2 to satisfy T^2=T (that is the composition of T with itself equals T again) without having T=Z or T=I, if so give an example of such a linear operator T, if not prove that it is not

Question

Is it possible for a linear operator T: R^2--> R^2 to satisfy T^2=T (that is the composition of T with itself equals T again) without having T=Z or T=I, if so give an example of such a linear operator T, if not prove that it is not

anonymous · Answer

what does T = Z mean?

anonymous · Answer

the zero operator, and T=I is the identity operator

anonymous · Answer

i assume T = I means T is the identity

anonymous · Answer

sure, put
$$T(x_1,x_2)=(x_1,0)$$ a projection 
in fact such a T with T^2=T is often called a "projection" even if it is not the one wrote

anonymous · Answer

*I wrote