Certain strongly clean matrices over local rings

We are concerned about various strongly clean properties of a kind of matrix subrings L-(s) (R) over a local ring R. Let R be a local ring, and let s is an element of C(R). We prove that A is an element of L-(s) (R) is strongly clean if and only if A or I-2 - A is invertible, or A is similar to a diagonal matrix in L-(s) (R). Furthermore, we prove that A is an element of L-(s) (R) is quasipolar A if and only if A is an element of GL(2) (R) or A is an element of L-(s)(R)(qnil) or A is similar to a diagonal matrix in