Let \(\phi\) be a Lorentz-scalar field.

(a) Show that the quantities \(T_{\mu u}=\partial_{\mu} \phi \partial_{u} \phi-\frac{1}{2} g_{\mu u}\left\{(\partial \phi)^{2}-\kappa^{2} \phi^{2}\right\}\) with \(\lambda \in \mathbb{R}\) are components of a Lorentz \((0,2)\) tensor field.

(b) Show that \(\partial_{\mu} T^{\mu u}=0\) if \(\phi(x)\) obeys the wave equation \(\left(\partial^{2}+\kappa^{2}\right) \phi=0\).