2-24. Let (M.g) be a compact Riemannian manifold (without boundary). A real number is called an eigenvalue of M if there exists a smooth function u on M, not identically zero, such that -Auu. In this case, u is called an eigenfunction corresponding to A. (a) Prove that 0 is an eigenvalue of M, and that all other eigenvalues are strictly positive. (b) Show that if u and v are eigenfunctions corresponding to distinct eigen- values, then uv dVg = 0. (Used on p. 149.)