= Elementary matrix
An elementary matrix is obtained by applying one <elementary row operation> to the <identity matrix>. Multiplying $A$ by it on the left performs the same row operation on $A$. Such a <matrix> is invertible: reverse a row swap, reverse a nonzero row scaling by its reciprocal, or reverse adding a multiple of another row by adding its negative. Right multiplication gives an <elementary column operation>. In particular these operations preserve <matrix rank>.
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