vim, 188 bytes

Result

AC

Duration

530ms

Code [DL]

00000000  56 47 4a 3a 6c 65 74 20  6c 3d 6d 61 70 28 73 70  |VGJ:let l=map(sp|
00000010  6c 69 74 28 67 65 74 6c  69 6e 65 28 31 29 2c 27  |lit(getline(1),'|
00000020  20 27 29 2c 27 73 74 72  32 6e 72 27 29 0a 3a 66  | '),'str2nr').:f|
00000030  6f 72 20 69 20 69 6e 20  72 61 6e 67 65 28 39 29  |or i in range(9)|
00000040  0a 6c 65 74 20 6c 5b 69  2b 33 5d 2d 3d 6c 5b 69  |.let l[i+3]-=l[i|
00000050  25 33 5d 0a 65 6e 64 66  6f 72 0a 67 67 56 47 63  |%3].endfor.ggVGc|
00000060  12 3d 28 6c 5b 31 31 5d  2a 28 6c 5b 37 5d 2a 6c  |.=(l[11]*(l[7]*l|
00000070  5b 33 5d 2d 6c 5b 34 5d  2a 6c 5b 36 5d 29 2d 6c  |[3]-l[4]*l[6])-l|
00000080  5b 31 30 5d 2a 28 6c 5b  33 5d 2a 6c 5b 38 5d 2d  |[10]*(l[3]*l[8]-|
00000090  6c 5b 35 5d 2a 6c 5b 36  5d 29 2b 6c 5b 39 5d 2a  |l[5]*l[6])+l[9]*|
000000a0  28 6c 5b 34 5d 2a 6c 5b  38 5d 2d 6c 5b 37 5d 2a  |(l[4]*l[8]-l[7]*|
000000b0  6c 5b 35 5d 29 29 2f 36  0a 1b 5a 5a              |l[5]))/6..ZZ|
000000bc

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>ggVGc<C-R>=(l[11]*(l[7]*l[3]-l[4]*l[6])-l[10]*(l[3]*l[8]-l[5]*l[6])+l[9]*(l[4]*l[8]-l[7]*l[5]))/6<NL><Esc>ZZ

stdin

39 97 54
66 04 55
45 76 23
83 91 40

stdout

20474

stderr

strace