Let A be an $\displaystyle m \times n$ matrix. If $\displaystyle k \leq m$ and $\displaystyle l \leq n$ , then a $\displaystyle k \times l$ matrix $\displaystyle B$ is said

to be a submatrix of $\displaystyle A$, if$\displaystyle B$can be obtained from $\displaystyle A$ by deleting some set of $\displaystyle m-k$rows and $\displaystyle n-l$columns of $\displaystyle A$.

if we define the determinantal rank of $\displaystyle A$ to be the largest $\displaystyle k$for which $\displaystyle A$ has a$\displaystyle k \times k$

submatrix with non-zero determinant. Show that this is equal to the usual row or

column rank of $\displaystyle A$.