Some results on the group inverse of the block matrix with a sub-block of linear combination or product combination of matrices over skew fields

摘要

Let K be any skew field and K m×n be the set of all the m × n matrices over K. In this article, necessary and sufficient conditions are given for the existence of the group inverses of block matrix , where and exist, A = c ₁ B + c ₂ C, non-zero elements c ₁ and c ₂ are in the centre of K and block matrix , where A = B k C l , k and l are positive integers. Then the representations of the group inverses of these block matrices are also given.