On nonsingularity of combinations of two group invertible matrices and two tripotent matrices.

Let T 1 and T 2 be two n × n tripotent matrices and c 1, c 2 two nonzero complex numbers. We mainly study the nonsingularity of combinations T = c 1 T 1 + c 2 T 2 − c 3 T 1 T 2 of two tripotent matrices T 1 and T 2, and give some formulae for the inverse of c 1 T 1 + c 2 T 2 − c 3 T 1 T 2 under some conditions. Some of these results are given in terms of group invertible matrices. [ABSTRACT FROM AUTHOR]