Inverse the value place of matrix - matrix

Question

I'am trying to inverse a matrix(actually it is a s-box for AES). The dimensions are 10*16 (10 rows and 16 columns)
The box is filled up with numbers and I want to inverse this box
like this :
a[0][0]=63 (for example in the first row/column the value is 63)
after inverse operation:
a[6][3]=00 i want change it with this
I tried some algorithms but didn't work

Answer 1

Well, in the page you linked the matrix is 16x16 and it's stored in a single 1D array of hexadecimal values. The inversion is the easiest part of that algorythm. I'll give you a c++ code for example:
#include <iostream>
#include <iomanip>
#define ROWS 16
#define COLS 16
#define N_ELEMENTS 256
void Invert(unsigned char * in, unsigned char * out) {
for ( int i = 0; i < N_ELEMENTS; i++ ) out[in[i]] = i;
}
void showMatrix(unsigned char * m) {
for ( int i = 0; i < ROWS; i++) {
for (int j = 0; j < COLS; j++) {
std::cout << " " << std::setbase(16) << std::setfill('0') << std::setw(2)
<< (unsigned int)m[i*COLS + j];
}
std::cout << std::endl;
}
}
int main() {
unsigned char s[256] = {
0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16
};
unsigned char inv[256];
Invert(s,inv);
std::cout << "This is the original matrix:\n";
showMatrix(s);
std::cout << "\nThis is the inverted matrix:\n";
showMatrix(inv);
return 0;
}
The output is this:
This is the original matrix:
63 7c 77 7b f2 6b 6f c5 30 01 67 2b fe d7 ab 76
ca 82 c9 7d fa 59 47 f0 ad d4 a2 af 9c a4 72 c0
b7 fd 93 26 36 3f f7 cc 34 a5 e5 f1 71 d8 31 15
04 c7 23 c3 18 96 05 9a 07 12 80 e2 eb 27 b2 75
09 83 2c 1a 1b 6e 5a a0 52 3b d6 b3 29 e3 2f 84
53 d1 00 ed 20 fc b1 5b 6a cb be 39 4a 4c 58 cf
d0 ef aa fb 43 4d 33 85 45 f9 02 7f 50 3c 9f a8
51 a3 40 8f 92 9d 38 f5 bc b6 da 21 10 ff f3 d2
cd 0c 13 ec 5f 97 44 17 c4 a7 7e 3d 64 5d 19 73
60 81 4f dc 22 2a 90 88 46 ee b8 14 de 5e 0b db
e0 32 3a 0a 49 06 24 5c c2 d3 ac 62 91 95 e4 79
e7 c8 37 6d 8d d5 4e a9 6c 56 f4 ea 65 7a ae 08
ba 78 25 2e 1c a6 b4 c6 e8 dd 74 1f 4b bd 8b 8a
70 3e b5 66 48 03 f6 0e 61 35 57 b9 86 c1 1d 9e
e1 f8 98 11 69 d9 8e 94 9b 1e 87 e9 ce 55 28 df
8c a1 89 0d bf e6 42 68 41 99 2d 0f b0 54 bb 16
This is the inverted matrix:
52 09 6a d5 30 36 a5 38 bf 40 a3 9e 81 f3 d7 fb
7c e3 39 82 9b 2f ff 87 34 8e 43 44 c4 de e9 cb
54 7b 94 32 a6 c2 23 3d ee 4c 95 0b 42 fa c3 4e
08 2e a1 66 28 d9 24 b2 76 5b a2 49 6d 8b d1 25
72 f8 f6 64 86 68 98 16 d4 a4 5c cc 5d 65 b6 92
6c 70 48 50 fd ed b9 da 5e 15 46 57 a7 8d 9d 84
90 d8 ab 00 8c bc d3 0a f7 e4 58 05 b8 b3 45 06
d0 2c 1e 8f ca 3f 0f 02 c1 af bd 03 01 13 8a 6b
3a 91 11 41 4f 67 dc ea 97 f2 cf ce f0 b4 e6 73
96 ac 74 22 e7 ad 35 85 e2 f9 37 e8 1c 75 df 6e
47 f1 1a 71 1d 29 c5 89 6f b7 62 0e aa 18 be 1b
fc 56 3e 4b c6 d2 79 20 9a db c0 fe 78 cd 5a f4
1f dd a8 33 88 07 c7 31 b1 12 10 59 27 80 ec 5f
60 51 7f a9 19 b5 4a 0d 2d e5 7a 9f 93 c9 9c ef
a0 e0 3b 4d ae 2a f5 b0 c8 eb bb 3c 83 53 99 61
17 2b 04 7e ba 77 d6 26 e1 69 14 63 55 21 0c 7d

Answer 2

Something like this should do the trick, although there's probably a more efficient way.
Matrix Invert(Matrix in)
{
Matrix out = new Matrix[10][16];
for(int i = 0; i < 10; i++)
{
for(int j = 0; j < 16, j++)
{
int row = Math.Floor(in[i][j] / 16);
int column = in[i][j] % 16;
out[row][column] = i * 16 + j;
}
}
return out;
}