Suppose $x = 0$ is the only solution to the matrix equation $Ax = 0$ where $A$ is $m \times n$, $x$ is $n \times 1$, and $0$ is $m \times 1$. Then (i) The rank of $A$ is $n$, and (ii) $m \times n$
Why is this the case, can somebody give me an intuition on the two implications.