Trouble with $4\times4$ matrix determinant $$
    \begin{vmatrix}
    1 & -6 & 7 & 5 \\
    0 & 0 & 3 & 0 \\
    3 & -2 & -8 & 6\\
    2 & 0 & 5 & 4\\
    \end{vmatrix}
$$
Clearly I want to expand along the second row yielding: 
$((-1)^5)3$ times the following matrix
$$
    \begin{vmatrix}
    1 & -6 & 5 \\
    3 & -2 & 6 \\
    2 & 0 & 4 \\
    \end{vmatrix}
$$
and then breaks down into several smaller matrices:
2 times 
$$
    \begin{vmatrix}
    -6 & 5 \\
    -2 & 6 \\
    \end{vmatrix}
$$
and 4 times
$$
    \begin{vmatrix}
    1 & -6 \\
    3 & -2 \\
    \end{vmatrix}
$$
which should come out to be $-3[(2(-36+10))+(4(-2+18))]$
$-3[(2(-16))+(4(16))]$
$-3(-32+64)=32 \times -3$
but the answer is -36 I don't know what went wrong?

Another way to approach this 4x4 matrix is to row reduce to a triangular matrix with zeros underneath the diagonal.
\begin{bmatrix}1&-6&7&5\\0&0&3&0\\3&-2&-8&6\\2&0&5&4\end{bmatrix} 
Row reducing to the triangular matrix yields:
\begin{bmatrix}1&-6&7&5\\0&16&-29&-9\\0&0&3&0\\0&0&0&\frac{3} {4}\end{bmatrix}
From here, we can multiply the numbers in the diagonal:
-(1 $\cdot$ 16 $\cdot$ 3 $\cdot$ $\frac{3} {4}$) = -36
