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(August 22, 2005), Linear Algebra and Its Applications (3rd ed.), Addison Wesley, ISBN 978-3-7 Axler, Sheldon Jay (1997), Linear Algebra Done Right (2nd ed.), Springer-Verlag, ISBN 9-0.

Row-addition transforms satisfy the Steinberg relations.

Therefore, for a square matrix A (of the correct size) we have det = det.

The matrix and its inverse are triangular matrices.

L ij( m) −1 = L ij(− m) (inverse matrix).

These transformations are a kind of shear mapping, also known as a transvections.

And A L ij( m) is the matrix produced from A by adding m times column j to column i. So L ij( m) A is the matrix produced from A by adding m times row i to row j.