Solving for the determinant of a matrix? I know the rules of solving for the determinants of a matrix and I totally thought I was doing this right, but the answer output is incorrect.
I took the approach that I was adding the $a, b$ and $c$, so nothing would change. However, I notice I am multiplying the second row by scalars, so I just figured it would be $-4^3 \cdot (1)$ for $-64$. Can someone explain the intuition behind the solution please. Thanks for the help.
Never mind, I realized my mistake was I was taking the value of $-4^3$, however, the entire row was just being multiplied by the value of $-4$. Therefore, the final answer came out to be $-4$.  

Given $$\det\begin{bmatrix}
a&b&c\\
d&e&f\\
g&h&i
\end{bmatrix}=1$$
  Find the determinat
  $$\det\begin{bmatrix}
a&b&c\\
-4d+a&-4e+b&-4f+c\\
g&h&i
\end{bmatrix}$$


If ${\rm det}\ A=1$, can you calculate 
  $$  {\rm det}\ (\left(  \begin{matrix} 1&0&0\\ 1 &-4 &0 \\ 0&0&1 \end{matrix} \right) A) $$
