Let $A$ be a matrix with linearly independent columns.

Select the best statement.

A. The equation $A{\bf x} = {\bf 0}$ always has nontrivial solutions.
B. The equation $A{\bf x} = {\bf 0}$ has nontrivial solutions precisely when it has more rows than columns.
C. The equation $A{\bf x} = {\bf 0}$ never has nontrivial solutions.
D. The equation $A{\bf x} = {\bf 0}$ has nontrivial solutions precisely when it is a square matrix.
E. The equation $A{\bf x} = {\bf 0}$ has nontrivial solutions precisely when it has more columns than rows.
F. There is no easy way to tell if such an equation has nontrivial solutions.
G. none of the above