Suppose $C$$A$ = $I$. ($C$ and $A$ may not be square.) Show that the equation Ax = 0 has only the trivial solution. Why can $A$ not have more columns than rows?
I understand having only trivial solutions implies that there's linear independence, and the second part of the question most likely implies there can't be any free variables, but I can't pinpoint exactly the answer they are looking for.