==========================================================
		C source code
==========================================================

#include "stdafx.h"
#include <complex>

double determinamt(double* pa, int n);
void inversematrix(double* pa, double* px, int n);
void Minor(double* pa, double* pm, int n, int k, int l);

int _tmain(int argc, _TCHAR* argv[])
{
	int i, j, k;

	double a[8][8]={0.6791, 0.0987, 0.4942, 0.0305, 0.8055, 0.9787, 0.5216, 0.973,
			0.3955, 0.2619, 0.7791, 0.7441, 0.5767, 0.7127, 0.0967, 0.649,
			0.3674, 0.3354, 0.715,  0.5,    0.1829, 0.5005, 0.8181, 0.8003,
			0.988,  0.6797, 0.9037, 0.4799, 0.2399, 0.4711, 0.8175, 0.4538,
			0.0377, 0.1366, 0.8909, 0.9047, 0.8865, 0.0596, 0.7224, 0.4324,
			0.8852, 0.7212, 0.3342, 0.6099, 0.0287, 0.682,  0.1499, 0.8253,
			0.9133, 0.1068, 0.6987, 0.6177, 0.4899, 0.0424, 0.6596, 0.0835,
			0.7962, 0.6538, 0.1978, 0.8594, 0.1679, 0.0714, 0.5186, 0.1332};

	double b[8][8]={2.0373, 0.2961, 1.4826, 0.0915, 2.4165, 2.9361, 1.5648, 2.919,
			1.1865, 0.7857, 2.3373, 2.2323, 1.7301, 2.1381, 0.2901, 1.947,
			1.1022, 1.0062, 2.145,  1.5,    0.5487, 1.5015, 2.4543, 2.4009,
			2.964,  2.0391, 2.7111, 1.4397, 0.7197, 1.4133, 2.4525, 1.3614,
			0.1131, 0.4098, 2.6727, 2.7141, 2.6595, 0.1788, 2.1672, 1.2972,
			2.6556, 2.1636, 1.0026, 1.8297, 0.0861, 2.046,  0.4497, 2.4759,
			2.7399, 0.3204, 2.0961, 1.8531, 1.4697, 0.1272, 1.9788, 0.2505,
			2.3886, 1.9614, 0.5934, 2.5782, 0.5037, 0.2142, 1.5558, 0.3996};

	double c[8][8]={0.5202, 1.9706, 1.1172, 0.8074, 1.999, 0.0978,  0.4692, 1.7685,
			0,	1.8839, 0.5944, 1.2685, 1.6174, 1.6836, 2.5666, 0.6786,
			0,	0,	1.4691, 1.6436, 2.0943, 2.6456, 1.9343, 1.1539,
			0,	0,	0,	2.8282, 1.9996, 2.0075, 1.1288, 1.749,
			0,	0,	0,	0,	0.5344, 0.5713, 0.5728, 0.7554,
			0,	0,	0,	0,	0,	1.1067, 1.2848, 0.8713,
			0,	0,	0,	0,	0,	0,	1.4461, 1.8513,
			0,	0,	0,	0,	0,	0,	0,	0.7958};

	double det, deta, detb, detc, tra, trb, trab, trba;
	double  ab[8][8];
	double  ba[8][8];
	double  at[8][8];
	double  xa[8][8];
	double  xb[8][8];
	double  xc[8][8];
	double xab[8][8];
	double xba[8][8];

/* (i) */
	printf("(i) \n");

	det = determinamt((double*)&a[0][0], 8);
	deta = det;
	printf("determinamt A  = %13.10f\n", det);
	

	det = determinamt((double*)&b[0][0], 8);
	detb = det;
	printf("determinamt B  = %13.10f\n", det);

/* (ii) */
	printf("(ii) \n");
	
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			ab[i][j]=0;
			for(k=0; k<8; k++){
				ab[i][j] += a[i][k]*b[k][j];
			}
		}
	}

	det = determinamt((double*)&ab[0][0], 8);

	printf("determinamt AB = %13.10f\n", det);

	printf("det A * det B  = %13.10f\n", deta*detb);

	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			ba[i][j]=0;
			for(k=0; k<8; k++){
				ba[i][j] += b[i][k]*a[k][j];
			}
		}
	}

	det = determinamt((double*)&ba[0][0], 8);

	printf("determinamt BA = %13.10f\n", det);

/* (iii) */
	printf("(iii) \n");

	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			at[j][i]=a[i][j];
		}
	}

	det = determinamt((double*)&at[0][0], 8);

	printf("determinamt At = %13.10f\n", det);
	printf("determinamt A  = %13.10f\n", deta);

/* (iv) */
	printf("(iv) \n");

	det = determinamt((double*)&c[0][0], 8);
	printf("determinamt C  = %13.10f\n", det);

	detc=1;
	for(i=0; i<8; i++){
		detc *= c[i][i];
	}

	printf("detC(diagonal) = %13.10f\n", detc);

/* (v) */
	printf("(v) \n");

	inversematrix((double*)&a[0][0], (double*)&xa[0][0], 8);
	inversematrix((double*)&b[0][0], (double*)&xb[0][0], 8);
	inversematrix((double*)&c[0][0], (double*)&xc[0][0], 8);

	printf("A inverse \n", detc);
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){	
			printf(" %7.4f", xa[i][j]);
		}
		printf("\n");
	}
	printf("B inverse \n", detc);
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", xb[i][j]);
		}
		printf("\n");
	}
	printf("C inverse \n", detc);
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){	
			printf(" %7.4f", xc[i][j]);
		}
		printf("\n");
	}

/* (vi) */
	printf("(vi) \n");

	inversematrix((double*)&ab[0][0], (double*)&xab[0][0], 8);

	printf("AB inverse \n", detc);
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){	
			printf(" %7.4f", xab[i][j]);
		}
		printf("\n");
	}

	for(i=0; i<8; i++){
		  for(j=0; j<8; j++){
			   xba[i][j]=0;
			   for (k = 0; k<8; k++) {
				xba[i][j]+=xb[i][k]*xa[k][j];
				}
		  }
	 }

	printf("B inv A inv \n", detc);
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){	
			printf(" %7.4f", xba[i][j]);
		}
		printf("\n");
	}

/* (vii) */
	printf("(vii) \n");
	
	tra=0;
	for(i=0; i<8; i++){
		tra += a[i][i];
	}
	printf("tr A = %13.10f\n", tra);

	trb=0;
	for(i=0; i<8; i++){
		trb += b[i][i];
	}
	printf("tr B = %13.10f\n", trb);

/* (viii) */
	printf("(viii) \n");
	trab=0;
	for(i=0; i<8; i++){
		trab += ab[i][i];
	}
	printf("tr AB = %13.10f\n", trab);

	trba=0;
	for(i=0; i<8; i++){
		trba += ba[i][i];
	}
	printf("tr BA = %13.10f\n", trba);

	return 0;
}

void inversematrix(double* pa, double* px, int n)
{
	int i;
	int j;
	double det;
	double* pm = new double[(n-1)*(n-1)];

	det = determinamt(pa, n);

	for(i=0; i<n; i++){
		for(j=0; j<n; j++){
			/* Minor */
			Minor(pa, pm, n, i, j );
			*(px+(i+j*n)) = pow(double(-1),int(i+1+j+1)) * determinamt(pm, n-1) * (1.0 / det);
		}
	}
	delete [] pm;

	return ;

}

double determinamt(double* pa, int n)
{
	double det;

	if(n == 2){
		det   = (*(pa+0))     * (*(pa+3))     - (*(pa+1))     * (*(pa+2));
		return det;
	}

	int i;
	double* pm = new double[(n-1)*(n-1)];

	det = 0;

	for(i=0; i<n; i++){
	/* Minor */
		Minor(pa, pm, n, 0, i);
		det = det + pow(double(-1),int(1+i+1)) * (*(pa+(i))) * determinamt(pm, n-1);
	}
	delete [] pm;

	return det;
}

void Minor(double* pa, double* pm, int n, int k, int l)
{
	int i, j, x, y;

	x = 0;

	for(i=0; i<n; i++){
		if(i != k){	
			y = 0;
			for(j=0; j<n; j++){
				if(j != l){
					*(pm+(x*(n-1)+y)) = *(pa+(i*n+j));
					y ++;
				}
			}
			x ++;
		}
	}

	return ;

}

=============================================================
			Results
=============================================================

(i)
determinamt A  =  0.0575731673
determinamt B  = 377.7375504427
(ii)
determinamt AB = 21.7475471749
det A * det B  = 21.7475471749
determinamt BA = 21.7475471749
(iii)
determinamt At =  0.0575731673
determinamt A  =  0.0575731673
(iv)
determinamt C  =  2.7713303057
detC(diagonal) =  2.7713303057
(v)
A inverse
  0.0803 -0.5595 -0.4300 -0.2613 -0.1820  0.9571  1.2667 -0.5204
  0.0654 -0.7137 -1.5671  1.8005  1.1801  0.5478 -1.7933  0.1797
 -0.7694  0.2345 -0.3623  1.1102  0.4195  0.4683  0.3448 -1.6066
 -0.3972  1.1915  1.0716 -1.2642 -0.7000 -0.6733  0.3728  1.1754
  0.8277 -0.5411 -1.6324  0.4060  1.2096  0.2101 -0.5095  0.1059
  0.5489  2.7082  1.3017  0.0264 -2.3266 -3.0920 -0.9484  2.1888
  0.4276  0.0035  1.3685 -0.1209 -0.6684 -1.5978 -0.3047  1.3096
 -0.0983 -1.9715 -0.0821 -0.8223  1.5133  2.8524  0.6502 -1.8672
B inverse
  0.0268 -0.1865 -0.1433 -0.0871 -0.0607  0.3190  0.4222 -0.1735
  0.0218 -0.2379 -0.5224  0.6002  0.3934  0.1826 -0.5978  0.0599
 -0.2565  0.0782 -0.1208  0.3701  0.1398  0.1561  0.1149 -0.5355
 -0.1324  0.3972  0.3572 -0.4214 -0.2333 -0.2244  0.1243  0.3918
  0.2759 -0.1804 -0.5441  0.1353  0.4032  0.0700 -0.1698  0.0353
  0.1830  0.9027  0.4339  0.0088 -0.7755 -1.0307 -0.3161  0.7296
  0.1425  0.0012  0.4562 -0.0403 -0.2228 -0.5326 -0.1016  0.4365
 -0.0328 -0.6572 -0.0274 -0.2741  0.5044  0.9508  0.2167 -0.6224
C inverse
  1.9223 -2.0108 -0.6483  0.7298 -1.2952  3.7836  0.3941 -7.0512
 -0.0000  0.5308 -0.2148 -0.1133 -0.3411  0.0874 -0.5090  1.5198
  0.0000 -0.0000  0.6807 -0.3956 -1.1874 -0.2967  0.1322  1.0268
 -0.0000  0.0000 -0.0000  0.3536 -1.3230  0.0416  0.2111 -0.0579
  0.0000 -0.0000  0.0000 -0.0000  1.8713 -0.9660  0.1170 -0.9909
 -0.0000  0.0000 -0.0000  0.0000 -0.0000  0.9036 -0.8028  0.8783
  0.0000 -0.0000  0.0000 -0.0000  0.0000 -0.0000  0.6915 -1.6087
 -0.0000  0.0000 -0.0000  0.0000 -0.0000  0.0000 -0.0000  1.2566
(vi)
AB inverse
  0.4573  1.2211  1.3457 -0.3164 -1.5845 -2.2537 -0.2266  1.6492
  0.3141  0.9117 -0.0316 -1.5852 -0.3828 -0.1141  0.3453  1.0372
  0.2336  1.9036  0.6043  0.0932 -1.2520 -2.6728 -0.9712  2.2834
 -0.3938 -1.8814 -0.9198  1.2412  1.6875  2.1058 -0.3653 -2.0137
  0.6714 -0.0907 -0.2962 -1.0150 -0.0944  0.0596  0.3386  0.7649
 -1.6781 -4.4455 -2.2093  1.1444  3.9832  6.4769  0.7091 -4.7341
 -0.8865 -2.2045 -0.7760  0.0710  1.8932  3.3852  1.2541 -2.9917
  1.1776  3.6841  1.5219 -0.1430 -3.2778 -5.1750 -0.6041  3.2012
B inv A inv
  0.4573  1.2211  1.3457 -0.3164 -1.5845 -2.2537 -0.2266  1.6492
  0.3141  0.9117 -0.0316 -1.5852 -0.3828 -0.1141  0.3453  1.0372
  0.2336  1.9036  0.6043  0.0932 -1.2520 -2.6728 -0.9712  2.2834
 -0.3938 -1.8814 -0.9198  1.2412  1.6875  2.1058 -0.3653 -2.0137
  0.6714 -0.0907 -0.2962 -1.0150 -0.0944  0.0596  0.3386  0.7649
 -1.6781 -4.4455 -2.2093  1.1444  3.9832  6.4769  0.7091 -4.7341
 -0.8865 -2.2045 -0.7760  0.0710  1.8932  3.3852  1.2541 -2.9917
  1.1776  3.6841  1.5219 -0.1430 -3.2778 -5.1750 -0.6041  3.2012
(vii)
tr A =  4.4972000000
tr B = 13.4916000000
(viii)
tr AB = 54.7720830000
tr BA = 54.7720830000