obtain all non zero solutions for a linear system

Question

Is it possible to find the solutions of a non-symmetric, non-square matrix ? If so, how do I know if it has infinite, unique or no solutions ?? The given linear system is : $$\begin{bmatrix} 1 & -2 & -1 & 3\\[1ex] -2 & 4 & 5 & -5\\[1ex] 3 & -6 & -6 & 8 \end{bmatrix}\begin{bmatrix} x_1\\[1ex] x_2 \\[1ex] x_3\\[1ex] x_4 \end{bmatrix} = \begin{bmatrix} 0\\[1ex] 3\\[1ex] 2 \end{bmatrix}$$

Answer 1

Hint 1: if $Ax=b$ but $A$ is not square, then multiply both sides by $A^{\text{T}}$.

Hint 2: The third row of $A$ is actually the first row minus the second row, but the same is not true for $b$; that is a bad omen.