Eigenvalue/Eigenspace Problem

a) Let T be a linear operator on a vector space V and suppose T^2 = I.
What are the possible eigenvalues of T ?
b) Let T be the operator on C(R) (the space of continuous functions
on R) which is defined by T f(t) = f(−t). Find all eigenvalues and
characterize the corresponding eigenspaces.

*R in part b means the set of all real numbers