vim, 201 bytes

Result

AC

Duration

527ms

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

33 62 77
85 05 29
08 84 81
82 73 91

stdout

7925

stderr

strace