Let B = $\displaystyle \left(\begin{array}{c|ccc} 1 & 0 & ... & 0 \\\hline 0 & & & \\ \vdots & & B' & \\ 0 & & & \end{array}\right)$ ,

where B' is anmxnsubmatrix of B.

How do I prove the following:

If rank(B) =r, then rank(B') = r - 1.

Any help is appreciated. thanks.