vim, 200 bytes

Result

AC

Duration

499ms

Code [DL]

VGJ:let l=map(split(getline(1),' '),'str2nr')
:for i in range(9)
let l[i+3]-=l[i%3]
endfor
:call setline(1,(l[3]*(l[7]*l[11]-l[8]*l[10])+l[4]*(l[9]*l[8]-l[11]*l[6])+l[5]*(l[6]*l[10]-l[7]*l[9]))/6)
ZZ

Disassembly

VGJ:let l=map(split(getline(1),' '),'str2nr')<NL>:for i in range(9)<NL>let l[i+3]-=l[i%3]<NL>endfor<NL>:call setline(1,(l[3]*(l[7]*l[11]-l[8]*l[10])+l[4]*(l[9]*l[8]-l[11]*l[6])+l[5]*(l[6]*l[10]-l[7]*l[9]))/6)<NL>ZZ<NL>

stdin

71 37 42
77 29 94
41 18 87
89 09 06

stdout

12548

stderr

strace