let B be an n \times p matrix. For each  j \ (1 \leq j \leq p) let v_j denote the jth column of B. Prove that:

v_j =Be_j, where e_j is the jth standard vector of F^p

so far all I have is:

v_j = \left( \begin{array}{c}<br />
B_{1j} \\<br />
B_{2j} \\<br />
\vdots \\<br />
B_{mj}<br />
\end{array} \right) = Be_{j} \therefore v_j = Be_j

is this correct?