  Let $T$ be a tree on $n$ vertices whose edge weights are positive definite
matrices of order $s$. The squared distance matrix of $T$, denoted by $\Delta$,
is the $ns \times ns$ block matrix with $\Delta_{ij}=d(i,j)^2$, where $d(i,j)$
is the sum of the weights of the edges in the unique $(i,j)$-path. In this
article, we obtain a formula for the determinant of $\Delta$ and find
${\Delta}^{-1}$ under some conditions.
