How to find the determinant of a 5 x 5 matrix? Finding a 3x3 matrix is easy, but how can I find the determinant of this 5x5 matrix?? I just need an example of the first couple steps to mimic

$A =$
  $\begin{bmatrix} 7&1&9&-4&3\\0&-3&4&9&-6\\0&0&-6&-6&-9\\0&0&0&7&6\\0&0&0&0&2\end{bmatrix}$
then the $\det(A) = ?$

By the way, I did put the matrix in REF form and tried to multiply the diagonal and it didn't work at all.
I ended up getting 
$\begin{bmatrix} 464,679,936&0&0&0&0\\0&-14,112&0&0&0\\0&0&-168&0&0\\0&0&0&14&0\\0&0&0&0&2\end{bmatrix}$

Developing with respect the last row, you get that the determinant equals
$$2\cdot\begin{vmatrix}7&1&9&\!-4\\0&\!-3&4&9\\0&0&\!-6&\!-6\\0&0&0&7\end{vmatrix}$$
Again deloping the last row we get
$$2\cdot7\cdot\begin{vmatrix}7&1&9\\0&\!-3&4\\0&0&\!-6\end{vmatrix}=2\cdot7\cdot(-6)\cdot\begin{vmatrix}7&1\\0&\!-3\end{vmatrix}=-84(-21)=1,764$$
