Consider the following Gauss elimination:
$$A \to \underbrace{\left[\begin{array}{ccc} 1 &0 &0\cr 0 &1 &0\cr 0 &0 &-6 \end{array}\right]}_{E_1} A \to \underbrace{\left[\begin{array}{ccc} 1 &0 &0\cr 0 &0 &1\cr 0 &1 &0 \end{array}\right]}_{E_2} E_1 A \to \underbrace{\left[\begin{array}{ccc} 1 &0 &0\cr 0 &-6 &0\cr 0 &0 &1 \end{array}\right]}_{E_3} E_2E_1 A \to \underbrace{\left[\begin{array}{ccc} 1 &0 &1\cr 0 &1 &0\cr 0 &0 &1 \end{array}\right]}_{E_4} E_3E_2E_1 A=\left[\begin{array}{ccc} -2 &2 &-2\cr 0 &4 &5\cr 0 &0 &1 \end{array}\right]$$
What is the determinant of $A$?
$\det(A) =$