I cannot understand this statement which accompanies a standard result from Determinants and Matrices. The statement is as follows:
"If any line of a determinant D be passed over m parallel lines, the resulting determinant D' is equal to (-1)^m."
How can a determinant be passed over parallel lines?
That's a strange formulation indeed, but what I think it's trying to say is that $$\det(A')=(-1)^m \det(A)$$ if the matrix $A'$ is obtained from the matrix $A$ by moving one of the rows of $A$ past $m$ other rows.
(Google “row operation determinant” if you're not familiar with this.)