Abstarct: n this thesis, we show that if a ring R is a strongly clean ring, then so is every one-sided ideal of R. Also we study rings that M2(R) is not strongly clean. We will give necessary and sufficient conditions under which M n(R) is strongly clean for every n ≥ 1. Furthermore, we extend these results to triangular matrix ring. We determine when a 2×2 matrix ring over a commutative local ring is strongly clean. Several equivalent criteria are given for such a matrix to be strongly clean.