  The \emph{resistance matrix} of a simple connected graph $G$ is denoted by
$R$, and is defined by $R =(r_{ij})$, where $r_{ij}$ is the resistance distance
between the vertices $i$ and $j$ of $G$. In this paper, we consider the
resistance matrix of weighted graph with edge weights being positive definite
matrices of same size. We derive a formula for the determinant and the inverse
of the resistance matrix. Then, we establish an interlacing inequality for the
eigenvalues of resistance and Laplacian matrices. Using this interlacing
inequality, we obtain the inertia of the resistance matrix.
