Strongly clean matrix rings over commutative local rings

We will completely characterize the commutative local rings for which Mn(R)Mn(R) is strongly clean, in terms of factorization in R[t]R[t]. We also obtain similar elementwise results which show additionally that for any monic polynomial f∈R[t]f∈R[t], the strong cleanness of the companion matrix of ff is equivalent to the strong cleanness of all matrices with characteristic polynomial ff.