On nonsingularity of combinations of three group invertible matrices and three tripotent matrices

Autores UPV
Revista Linear and Multilinear Algebra


Let T=c1T1+c2T2+c3T3-c4(T1T2+T3T1+T2T3), where T1, T2, T3 are three n x n tripotent matrices and c1, c2, c3, c4 are complex numbers with c1, c2, c3 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.