  In this paper, we study the expanding phenomena in the setting of higher
dimensional matrix rings. More precisely, we obtain a sum-product estimate for
large subsets and show that x+yz, x(y+z) are moderate expanders over the matrix
ring, and xy + z + t is strong expander over the matrix rings. These results
generalize recent results of Y.D. Karabulut, D. Koh, T. Pham, C-Y. Shen, and
the second listed author.
