Prove that interchange of two rows of a matrix can be accomplished by a finite sequence of elemenatary row operations of the other two types.(adsbygoogle = window.adsbygoogle || []).push({});

My proof :-

If ##A_k## is to be interchanged by ##A_l## then,

##\displaystyle \begin{align} A_k &\to A_l + A_k \\ A_l &\to - A_l \\ A_l &\to A_k + A_l \\ A_l &\to A_l + A_k \\ A_l &\to \dfrac12 A_l \\ A_k &\to - A_k \\ A_k &\to A_k + A_l \\ A_k &\to - A_k \end{align}##

I think this now interchanges original ##A_l## with ##A_k##.

Is this correct ?

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# B Proof of elementary row matrix operation.

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