cy, 72 bytes

Result

AC

Duration

566ms

Code [DL]

"\\#{require'matrix';p Matrix[*$<.map{|x|eval'A=1,'+x.split*?,}].det/6}"

stdin

52 53 71
17 41 25
05 63 59
89 36 23

stdout

6101

stderr

(eval):1: warning: already initialized constant Cy::A
(eval):1: warning: previous definition of A was here
(eval):1: warning: already initialized constant Cy::A
(eval):1: warning: previous definition of A was here
(eval):1: warning: already initialized constant Cy::A
(eval):1: warning: previous definition of A was here

strace