<s>[INST] Permutations of elements of a matrix I'm a bit confused about the second part of the question I'm working on. The question is as follows

Let A be the $4 \times 4$ matrix
  $$A=\begin{bmatrix}
a_{11} & a_{12} & a_{13}  & a_{14} \\ 
a_{21} & a_{22} & a_{23} & a_{24} \\ 
a_{31} & a_{32} & a_{33} & a_{34} \\ 
a_{41} & a_{42} & a_{43} & a_{44}
\end{bmatrix}$$
(a) Write out all of the permutations $\sigma \in S_4$ with $\sigma(1)=4$ (there are six of them)
(b) Using the general formula for det($A$), write out all the terms corresponding to the permutations you found in part (a)

From my notes I have

To describe $\sigma$ in $S_n$ write $1,2,...,n$
  $$\begin{pmatrix}
1 & 2 & 3 & \cdots & 5 \\ 
\sigma(1) & \sigma(2)  & \sigma(3) & \cdots & \sigma(n) 
\end{pmatrix}$$

So the six permutations I end up with are
$$\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 1 & 2 & 3
\end{pmatrix}
\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 2 & 1 & 3
\end{pmatrix}
\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 3 & 1 & 2
\end{pmatrix}
\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 3 & 2 & 1
\end{pmatrix}
\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 2 & 3 & 1
\end{pmatrix}
\begin{pmatrix}
1 & 2 & 3 & 4\\ 
4 & 1 & 3 & 2
\end{pmatrix}$$
Now, I am not sure about part (b). I have 6 different permutations of 4 numbers. What terms from the general formula for det($A$) correspond to the permutations I found?
 [/INST] I believe the following is meant:  
The general formula (complete expansion) of the determinant is:
$$\det A = \sum_{\textrm{permutations p}} \left( \textrm{sign p} \right) a_{1, p_1} a_{2, p_2} \textrm{...} a_{n, p_n}.$$
In the case of your first permutation, the term would thus be:  
$$\left( -1 \right) a_{1, 4} a_{2, 1} a_{3,2} a_{4, 3},$$
with the others being similarly translated. 
</s>