Answer to Question #23765 in Linear Algebra for Matthew Lind
correspondence with elementary row and column operations of matrix. Thus, as it
is known, every elementary row/column operation preserves rank of matrix. So, matrix
Q=E1*E2*...*En, where each Ei is elementary matrix, AQ=(...((A*E1)*E2)*...)*En
and in every bracket rank is equal rank of matrix A.
As rank(A^T)=rank(A), then as P^T is also invertible,
rank(PAQ)=rank(Q^T * A^T * P^T)=rank(Q^T * A^T)=rank(AQ)=rank(A) and we are
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