I have a couple questions...

I don't understand when you're supposed to put a negative sign infront of the matrix when you switch two rows/columns of the matrix. When we first started matrices (reducing them,) we didn't do this, but now that we're taking determinants we do. I'm just not sure when I'm supposed to place a negative sign in front and when not to. (I'm talking about when two rows/columns of the matrix are switched.)

Also, when finding the determinant of a matrix, we can reduce the matrix by removing a factor of a row/column and placing it on the outside of the matrix. This must be done for EACH row/column when using determinants, but when we first did it, we could remove one factor and it would effect the WHOLE matrix, not just one row/column.

Any explanations?