Prove that $E$ is self adjoint iff $EE^*=E^*E$ where $E$ is a projection .

Question

I dont want the rigorous proof but I want the geometric intuition of the statement.

Now I know if $E$ is a projection operator (where $V$ is given to be finite dimensional) then $$V = R(E) \bigoplus K(E)$$

Since, it is a self adjoint operator so I am also aware of the fact that there exists an orthonormal basis of eigen vectors of $E$ but then I cant really find the geometric intuition of $EE^*=E^*E$.