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===1. Row switching transformations===
This transformation, ''T<sub>ij</sub>'', switches all matrix elements on row i with their counterparts on row j. The matrix resulting in this transformation is:<br>
:<math>
T_{i,j} = \begin{bmatrix} 1 & & & & & & & \\ & \ddots & & & & & & \\ & & 0 & & 1 & & \\ & & & \ddots & & & & \\ & & 1 & & 0 & & \\ & & & & & & \ddots & \\ & & & & & & & 1\end{bmatrix},\quad </math>
====Properties====
:*The inverse of this matrix is itself: ''T<sub>ij</sub><sup>-1</sup>=T<sub>ij</sub>''.
:*When applied to a matrix ''A'': ''det[TA]=-det[A]''.
:*The matrix and its gdgdginverse are lower triangular matrices.
===2. Row multiplying transformations===
