  A method of constructing $n^{2}\times n^{2}$ matrix solutions(with $n^{3}$
matrix elements) of Temperley-Lieb algebra relation is presented in this paper.
The single loop of these solutions are $d=\sqrt{n}$. Especially, a
$9\times9-$matrix solution with single loop d=$\sqrt{3}$ is discussed in
detail. An unitary Yang-Baxter $\breve{R}(\theta,q_{1},q_{2})$ matrix is
obtained via the Yang-Baxterization process. The entanglement property and
geometric property (\emph{i.e.} Berry Phase) of this Yang-Baxter system are
explored.
