Abstract.A ring R with identity is called strongly clean if every element of R is the sum of an idempotent and a unit that commute. For a commutative local ring R, n = 3, 4, and m, k, s ∈ ގ it is proved that ލ n (R) is strongly clean if and only if 1. Introduction. In this paper, R is an associative ring with identity. A ring R is called clean if for every element a ∈ R, there exist an idempotent e and a unit u in R such that a = e + u [10], and R is called strongly clean if in addition eu = ue [11]. By Han and Nicholson [8], the cleanness of the ring R implies that of the matrix ring ލ n (R) for any n ≥ 1. But if R is strongly clean, the matrix ring ލ n (R) with n > 1 may not be strongly clean. For example, the matrix ring ލ 2 ޚ( (2) ) is not strongly clean. This fact was observed by Sánchez Campos [12] and by Wang and Chen [13] independently (answering two questions of Nicholson in [11]). When is the matrix ring over a strongly clean ring still strongly clean? Recently, the authors found an equation condition [5, Theorem 8] for ލ 2 (R) over a commutative local ring to be strongly clean. In [4], the authors defined n-SRC ring (see Definition 2.1) and found the matrix ring ލ n (R) over a commutative local ring is strongly clean if and only if R is n-SRC.Let R [[x]] denote the formal power series ring with elements of the form ∞ i=0 r i x i , r i ∈ R, x 0 = 1. In [5, Theorem 9] it is proved that ލ 2 (R) over a commutative local ring R is strongly clean if and only if ލ 2 (R [[x]]) is strongly clean. This is equivalent to saying that if ލ 2 (R) is strongly clean, then the power series extension ލ( 2 (R)) [[x]] ( ∼ = ލ 2 (R[[x]])) is also strongly clean. However, it is not known, whether or not R [[x]] is also strongly clean wherever R is a strongly clear ring.