<s>[INST] Find the determinant of the following $4 \times 4$ matrix 
Use a cofactor expansion across a row or column to find the determinant of the following matrix
$$B=\begin{pmatrix}1 &c&0&0\\0&1&c&0\\0&0&1&c\\c&0&0&1\end{pmatrix}$$
Clearly indicate the steps you take.

I have tried
$$\det B = 1 \det \begin{pmatrix}1 &c&0\\0&1&c\\0&0&1\end{pmatrix}+(-c) \det \begin{pmatrix}c &0&0\\1&c&0\\0&1&c\end{pmatrix}$$
$$ = \det\begin{pmatrix}1 &c\\0&1\end{pmatrix}+c(-c)det\begin{pmatrix}c &0\\1&c\end{pmatrix}$$
$$=1-c^4$$
 [/INST] Expanding $\det B$ on first column we have that 
$$\det B=1\det\begin{pmatrix}1 &c&0\\0&1&c\\0&0&1\end{pmatrix}-c\begin{pmatrix}c &0&0\\1&c&0\\0&1&c\end{pmatrix}=1-c^4$$
The determinant of triangular matrix is the product of the diagonal entries
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