### Abstract

This is a continuation of an earlier paper by the authors on generalized inverses over integral domains. The main results consist of necessary and sufficient conditions for the existence of a group inverse, a new formula for a group inverse when it exists, and necessary and sufficient conditions for the existence of a Drazin inverse. We show that a square matrix A of rank r over an integral domain R has a group inverse if and only if the sum of all r × r principal minors of A is an invertible element of R. We also show that the group inverse of A when it exists is a polynomial in A with coefficients from R.

Original language | English |
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Pages (from-to) | 31-47 |

Number of pages | 17 |

Journal | Linear Algebra and Its Applications |

Volume | 146 |

Issue number | C |

DOIs | |

Publication status | Published - 15-02-1991 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis

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## Cite this

Manjunatha Prasad, K., Bhaskara Rao, K. P. S., & Bapat, R. B. (1991). Generalized inverses over integral domains. II. group inverses and Drazin inverses.

*Linear Algebra and Its Applications*,*146*(C), 31-47. https://doi.org/10.1016/0024-3795(91)90018-R