Because, as fresh_42 pointed out, the claim is NOT TRUE!Why not start with the equality ##A^2=A## where ##A## is the matrix for the transformation ##T##, and prove the claim using the matrix algebra of transformations?
In terms of basic problem solving technique:Summary: If T^2 = T, where T is a linear operator on a nonzero vector space V, does this imply that either T equals the identity operator on V or that T is the zero operator on V?
I can't think of a counterexample.
And how does my idempotent example in post #2 fit into this scheme?... all idempotetent matrices are similar to this.
in reals, withAnd how does my idempotent example in post #2 fit into this scheme?