  For each two-dimensional vector space $V$ of commuting $n\times n$ matrices
over a field $\mathbb F$ with at least 3 elements, we denote by $\widetilde V$
the vector space of all $(n+1)\times(n+1)$ matrices of the form
$\left[\begin{smallmatrix}A&*\\0&0\end{smallmatrix}\right]$ with $A\in V$. We
prove the wildness of the problem of classifying Lie algebras $\widetilde V$
with the bracket operation $[u,v]:=uv-vu$. We also prove the wildness of the
problem of classifying two-dimensional vector spaces consisting of commuting
linear operators on a vector space over a field.
