[Math] Homogeneous and nonhomogeneous matrices basics

Question

If $A$ is an $m\times n$ matrix where $m\lt n$

The nonhomogeneous system $Ax=o$ has at least one solution and the homogeneous system $Ax=0$ has a unique solution.

Are the above statements true or false …please assist

Answer 1

If $m\lt n$ then the system has fewer equations ($m$) than unknowns ($n$) (variables) and it is not possible for the homogeneous system to have a unique solution. The nonhomogeneous system may not have a solution.