This paper is a study on the invertibility of the commutator of scalar-idempotent elements and scalar-involutory elements of a unitary ring.

本文研究在一有单位元的环倍幂等元的换位子与倍对元的换位子的可逆性问题。

The necessary and sufficient conditions of similarity of two idempotent matrices are proved, the idempotency of linear combinations of two idempotent matrices is discussed.

摘要数域上同阶幂等阵相似的充要条件是它们有相同的秩；给出幂等阵的相似标准型；讨论幂等阵的线性组仍是幂等阵的充要条件。