  Theorem 7 in Ref. [Linear Algebra Appl., 430, 1-6, (2009)] states sufficient
conditions to determine whether a pair generates the algebra of 3x3 matrices
over an algebraically closed field of characteristic zero. In that case, an
explicit basis for the full algebra is provided, which is composed of words of
small length on such pair. However, we show that this theorem is wrong since it
is based on the validity of an identity which is not true in general.
