Could you please help to organize the following table? The last two rows of the table are messy.

```
\begin{center}
\begin{tabular}{ ||c|c|| } 
    \hline
    \hline
    &\\
    Singular matrix    & Non-singular matrix   \\&\\
    \hline
    \hline
    &\\
     A matrix $A$ is singular if 
    $det(A)=0$ 
      & A matrix $A$ is non-singular 
      $det(A)\ne0$
      \\ &\\
    \hline
    &\\
    If $A$ is singular, then $A^{-1}$ is not defined  & If $A$ is non-singular, then $A^{-1}$ is defined \\&\\
    \hline
    &\\
    Rank of $A <$ order of $ A$. &Rank of $A=$ order of $A$. \\&\\
    \hline
    &\\
    Some rows and columns are linearly dependent. & All rows and columns are linearly independent  \\&\\
    \hline
    &\\
    If $A$ singular, then the system of equations\\ $A\bx=\bb$
    has either no solution or\\infinitely many solutions.
    & If A non-singular, then the system of equations\\& $A\bx=\bb$ has unique solutions.
     \\&\\
    \hline
    &\\
    Example: $
    \left[\begin{array}{ll}
    3 & 6  \\
    1 & 2 \\
    \end{array}\right]
    $ is singular because
    \\
    $\left|\begin{array}{ll}3 & 6 \\ 1 & 2\end{array}\right|=(3 \times 2)-(6 \times 1)$
    $=6-6=0$
     & Example: $
     \left[\begin{array}{ll}
     3 & 2  \\
     1 & -2 \\
     \end{array}\right]
     $ is non-singular because
     \\&
     $\left|\begin{array}{ll}3 & 2 \\ 1 & -2\end{array}\right|=(3 \times (-2))-(2 \times 1)$
     $=-8\ne0$&\\
    \hline
    \hline
\end{tabular}
\end{center}

```

[![enter image description here](https://i.stack.imgur.com/lQG27.png)](https://i.stack.imgur.com/lQG27.png)