Answer
Ax=0 has only the trivial solution. A cannot have more columns than rows.
Work Step by Step
Let CA=$I_{n}$ and Ax=0
Ax=0 => CAx=C*0=0
CA=$I_{n}$ => CAx=$I_{n}$x=0
=> x=0
=> Ax=0 has only the trivial solution
Since Ax=0 has only the trivial solution, the columns of A are linearly independent.
Assume A is linearly independent and let A have more columns than rows. Then A has more vectors than entries in each vector => A is linearly dependent, a contradiction.
A cannot have more columns than rows.
