From tensor calculus, we know that

\begin{equation} g^{\mu\nu}=\delta_{\lambda}^{\mu}\delta_{\phi}^{\nu}g^{\lambda\phi}.\tag{1} \end{equation} Based on (1), is the following true? \begin{equation} g^{\mu\nu}g_{\lambda\phi}^{}=\delta_{\lambda}^{\mu}\delta_{\phi}^{\nu}.\tag{2} \end{equation}