structural:scholar_edition, information:extraction
Transpose

The determinant of the transpose of A {\displaystyle A} equals the determinant of A:

This can be proven by inspecting the Leibniz formula. This implies that in all the properties mentioned above, the word "column" can be replaced by "row" throughout. For example, viewing an n × n matrix as being composed of n rows, the determinant is an n -linear function.