Balanced supply and demand is both necessary and sufficient for transportation feasibility

Consider the transportation problem: Min.
$z=\sum_{i=1}^m\sum_{j=1}^nc_{ij}x_{ij}$ subject to $\sum_jx_{ij}=a_i, \sum_ix_{ij}=b_j$ and $x_{ij}\ge0$. The existence of a feasible solution of the transportation problem is possible: (I) if $\sum a_i=\sum b_j$. (II) if and only if $\sum a_i=\sum b_j$. Then which of the following is true?