Products of commutators in matrix rings

Let R be a ring and let n≥ 2. We discuss the question of whether every element in the matrix ring Mₙ(R) is a product of (additive) commutators $[x,y]=xy-yx$, for x,y∈ Mₙ(R). An example showing that this does not always hold, even when R is commutative, is provided. If, however, R has Bass stable rank one, then under various additional conditions every element in Mₙ(R) is a product of three commutators. Further, if R is a division ring with infinite center, then every element in Mₙ(R) is a product of two commutators. If R is a field and a∈ Mₙ(R), then every element in Mₙ(R) is a sum of elements of the form $[a,x][a,y]$ with x,y∈ Mₙ(R) if and only if the degree of the minimal polynomial of a is greater than $2$.