Incorrectly solving the determinant of a matrix Compute $det(B^4)$, where $B = 
    \begin{bmatrix}
     1       & 0 & 1 \\
     1       & 1 & 2 \\
     1       & 2 & 1 
    \end{bmatrix}
$ 
I created
$C=\begin{bmatrix}
     1       & 2 \\
     1       & 1 \\
    \end{bmatrix}
$ and 
$
 D= \begin{bmatrix}
     1       & 1 \\
     1       & 2 \\
    \end{bmatrix}
$
$det(B) = -det(C) -2det(D) = -(1-2) - 2(2-1) = -(-1)-2(1)=1-2=1, 1^4=1$
However, the correct answer is 16. I'm confused on where I made my wrong turn 

Use row reduction to calculate the determinant:
\begin{align}
\begin{vmatrix}1&0&1\\1&1&2\\1&2&1\end{vmatrix}=\begin{vmatrix}1&0&1\\0&1&1\\0&2&0\end{vmatrix}=\begin{vmatrix}1&0&1\\0&1&1\\0&0&-2\end{vmatrix}
\end{align}
hence $\;\det B=1\cdot1\cdot(-2)=-2$, so $\;\det B^4=(\det B)^4=16$.
