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OpenStudy (anonymous):

If a matrix B results from a matrix A by applying an elementary row operation, is there always an elementary row operation that can be applied to B to recover A?

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OpenStudy (zarkon):

elementary matrices are invertable

OpenStudy (anonymous):

\begin{eqnarray*} B &=& E_1E_2...E_nA \\ E_n^{-1}...E_2^{-1}E_1^{-1}B &=& E_n^{-1}...E_2^{-1}E_1^{-1} E_1 E_2...E_nA \\ E_n^{-1}...E_2^{-1}E_1^{-1}B &=& E_n^{-1}...E_2^{-1} I E_2...E_nA \\ E_n^{-1}...E_2^{-1}E_1^{-1}B &=& I A = A \\ \end{eqnarray*}

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