Nodal Analysis Question
You need to be consistent with your signs and assumptions.

In writing the KCL equation for node A, you defined it as

\begin{gather}
I_1 + I_2 + I_3 = 0
\end{gather}

where \$I_1\$, \$I_2\$, and \$I_3\$ are all leaving the node (consistent with the arrows in your diagram). However, then you immediately define

\begin{gather}
I_3 = \frac{V_B - V_A}{2k\Omega}
\end{gather}

This is the negative of the convention you just established. I would go through and double-check all of your signs and make sure they are consistent with each other. I can see similar issues in the KCL equations for the other nodes as well. You get lucky a few times by having a double negative cancel out your mistake, but this is just getting the correct answer for the wrong reasons.