Suppose a matrix $A$ has columns that span ${\mathbb R}^n$.

Select the best statement.

A. Then the equation $A{\bf x}={\bf 0}$ cannot have nontrivial solutions.
B. Then the equation $A{\bf x}={\bf 0}$ will have nontrivial solutions only if one column is a multiple of another column.
C. Then the equation $A{\bf x}={\bf 0}$ must have nontrivial solutions.
D. Then the equation $A{\bf x}={\bf 0}$ will have nontrivial solutions precisely when it is not square.
E. Then the equation $A{\bf x}={\bf 0}$ can have nontrivial solutions, but the shape of the matrix will not give us that information.
F. none of the above