ruby, 84 bytes

Result

AC

Duration

551ms

Code [DL]

require'matrix'
x=$<.map{|l|Vector[*l.split.map(&:to_i),1]}
p -Matrix.rows(x).det/6

stdin

74 31 14
06 05 66
58 98 20
06 93 29

stdout

24442

stderr

strace