If A1,…,An are t×t matrices, let V(A1,…,An) denote the matrix [image omitted] . Let q be a prime power and let Fq denote the finite field with q elements. Let v(q,t) denote the biggest integer n for which there exist t×t matrices A1,…,An with entries in Fq, such that V(A1,…,An) is invertible. J. V. Brawley posed the problem of concretely determining v(q,t). This paper presents a solution to this problem.
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