I'll go out on a limb and suppose you're given the matrix
[tex]\mathbf A=\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}[/tex]
and you're asked to find the determinant of [tex]\mathbf B[/tex], where
[tex]\mathbf B=\begin{bmatrix}a&b&c\\-4d&-4e&-4f\\a+g&b+h&c+i\end{bmatrix}[/tex]
and given that [tex]\det\mathbf A=2[/tex].
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant [tex]k[/tex], then the determinant of the matrix is scaled by that same constant;
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that
[tex]\det\mathbf B=-4\det\mathbf A=-8[/tex]
