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:That is, ''T<sub>ij</sub>'' is the matrix produced by exchanging row ''i'' and row ''j'' of the identity matrix.
====Properties====
:*The inverse of this matrix is itself: ''T<sub>ij</sub><sup>-1</sup>=T<sub>ij</sub>''.▼
:*The matrix ''T<sub>ij</sub>'' is square.
▲:*The inverse of this matrix is itself: ''T<sub>ij</sub><sup>-1</sup>=T<sub>ij</sub>''.
:*Since the [[Determinant|determinant]] of the [[Identity_matrix|identity matrix]] is unity, ''det[T<sub>ij</sub>]=-1''. It follows that for any conformable square matrix ''A'': ''det[T<sub>ij</sub>A]=-det[A]''.
===2. Row multiplying transformations===
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