  2$\leftrightarrow$3 symmetry is realized by the breaking from alterating
group of degree 4 ($A4$) symmetry. $A4$ explains why the generation number is
three. However the mass matrices are realized in the form of the breaking to
$2\leftrightarrow 3$ symmetry $\times Z_3$, which leads us to $2\leftrightarrow
3$ symmetric mass matrix with vanishing (1,1) component. Thus the $3\times 3$
mass matrix model with $2\leftrightarrow 3$ symmetry and vanishing (1,1)
component has the group theoretical background as the symmetry in GUT model.
