Let A be an mxn matrix. If k=<m and p=<n, then a k x p matrix B is said to be a submatrix of A, if B can be obtained from A by deleting some set of m - k rows and n - p columns of A.
(For example,
if A =
1 2 3 4
5 6 7 8
9 10 11 12, then
6,
3
11,
1 2 4
5 6 8
9 10 12
are all examples of submatrices of A.)
Define the determinantal rank of A to be the largest k for which A has a k x k submatrix with nonzero determinant, Show that this is equal to the usual row or column rank of A.