Find the volume of the parallelepiped with one vertex at the origin and adjacent

Setup the matrix A, where the columns are the vectors given.
$A=\left[\begin{array}{ccc}1& -2& -1\\ 3& 0& 3\\ 0& 2& -1\end{array}\right]$
The volume of the parallelepiped is equal to the absolute value of the determinant of A.
Volume $=|det(A)|$
So lets calculate the determinant. Expanding along the first column (because ${\displaystyle A_{3,1}=0}$ gives us two terms, but i'll show it for clarification)gives us to shown calculation.
$A=\left|\begin{array}{ccc}1& -2& -1\\ 3& 0& 3\\ 0& 2& -1\end{array}\right|=\left|\begin{array}{cc}0& 3\\ 2& -1\end{array}\right|-3\left|\begin{array}{cc}-2& -1\\ 2& -1\end{array}\right|+0\left|\begin{array}{cc}-2& -1\\ 0& 3\end{array}\right|=-6-12=-18$
Volume of the parallelepiped is 18.
Results:
Volume of the parallelepiped is 18.