  Verbally prime algebras are important in PI theory. They are well known over
a field $K$ of characteristic zero: 0 and $K<T>$ (the trivial ones), $M_n(K)$,
$M_n(E)$, $M_{ab}(E)$. Here $K<T>$ is the free associative algebra with free
generators $T$, $E$ is the infinite dimensional Grassmann algebra over $K$,
$M_n(K)$ and $M_n(E)$ are the $n\times n$ matrices over $K$ and over $E$,
respectively. Moreover $M_{ab}(E)$ are certain subalgebras of $M_{a+b}(E)$,
defined below. The generic algebras of these algebras have been studied
extensively. Procesi gave a very tight description of the generic algebra of
$M_n(K)$. The situation is rather unclear for the remaining nontrivial verbally
prime algebras.
  In this paper we study the centre of the generic algebra of $M_{11}(E)$ in
two generators. We prove that this centre is a direct sum of the field and a
nilpotent ideal (of the generic algebra). We describe the centre of this
algebra. As a corollary we obtain that this centre contains nonscalar elements
thus we answer a question posed by Berele.
