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Abstract
Let T = c 1 T 1 + c 2 T 2 + c 3 T 3 − c 4(T 1 T 2 + T 3 T 1 + T 2 T 3), where T 1, T 2, T 3 are three n × n tripotent matrices and c 1, c 2, c 3, c 4 are complex numbers with c 1, c 2, c 3 nonzero. In this article, necessary and sufficient conditions for the nonsingularity of such combinations are established and some formulae for the inverses of them are obtained. Some of these results are given in terms of group invertible matrices.
Acknowledgments
We would like to thank the referee for his/her careful reading. The first author was supported by the Vicerrectorado de Investigación U.P.V. PAID 06-2010-2285.