The Group Involutory Matrix of the Combinations of Two Idempotent Matrices

Abstract

We discuss the following problem: when $aP+bQ+cPQ+dQP+ePQP+fQPQ+gPQPQ$ of idempotent matrices $P$ and $Q$, where $a,b,c,d,e,f,g\in ℂ$ and $a\ne 0,b\ne 0$, is group involutory.