Question: A submatrix of a given matrix A is one that we get by deleting some of the rows and columns of A. Thus, the first

A submatrix of a given matrix A is one that we get by deleting some of the rows and columns of A. Thus, the first matrix here is a submatrix of the second.

Prove that for any square matrix, the rank of the matrix is r if and only if r is the largest integer such that there is an r Ã— r submatrix with a nonzero determinant.

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