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Determinant of a 3x3 matrix

A=[234−2−22−1−14]\text A = \left[\begin{array}{rrr}2 & 3 & 4 \\ -2 & -2 & 2 \\ -1 & -1 & 4\end{array}\right]
What is the determinant of A\text A?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}