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Question

Let A ϵ M_{nxn} (F) be nonzero. For any m(1≤m≤n), an m x m submatrix of A is obtained by deleting any n-m rows and any n-m columns from A. Let k (1≤k≤n) denote the largest integer such that some k x k submatrix of A has a nonzero determinant. Prove rank (A)=k.

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