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C++ Source Code:
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int _tmain(int argc, _TCHAR* argv[])
{
	int i;
	int j;
	int k;

	double a[8][4]={0.5688, 0.1656, 0.229,  0.1067,
			0.4694, 0.602,  0.9133, 0.9619,
			0.0119, 0.263,  0.1524, 0.0046,
			0.3371, 0.6541, 0.8258, 0.7749,
			0.1622, 0.6892, 0.5383, 0.8173,
			0.7943, 0.7482, 0.9961, 0.8687,
			0.3112, 0.4505, 0.0782, 0.0844,
			0.5285, 0.0838, 0.4427, 0.3998};

	double b[4][8]={0.2769, 0.6948, 0.4387, 0.1869, 0.7094, 0.6551, 0.9597, 0.7513,
			0.0462, 0.3171, 0.3816, 0.4898, 0.7547, 0.1626, 0.3404, 0.2551,
			0.0971, 0.9502, 0.7655, 0.4456, 0.276,  0.119,  0.5853, 0.506,
			0.8235, 0.0344, 0.7952, 0.6463, 0.6797, 0.4984, 0.2238, 0.6991};

	double c[4][8]={0.8909, 0.1493, 0.8143, 0.1966, 0.3517, 0.9172, 0.3804, 0.5308,
			0.9593, 0.2575, 0.2435, 0.2511, 0.8308, 0.2858, 0.5678, 0.7792,
			0.5472, 0.8407, 0.9293, 0.616,  0.5853, 0.7572, 0.0759, 0.934,
			0.1386, 0.2543, 0.35,   0.4733, 0.5497, 0.7537, 0.054,  0.1299};

	double d[4][4]={3.2090,  -2.5401,  -0.5887, -1.3159,
			-9.4480, 14.7505,  -17.3511, 16.3668,
			-5.5400, -1.1995,  4.5043,   3.5049,
			12.0418, -10.3090, 11.8869, -17.4378};

	double    x[4][8];
	double    y[8][8];
	double    z[8][8];
	double   ab[8][8];
	double   ca[4][4];
	double   ac[8][8];
	double   ba[4][4];
	double   ad[8][4];
	double  abt[8][8];
	double  cat[4][4];
	double badd[4][4];
	double bbad[4][4];

/* A(B+C) */

	 for(i=0; i<4; i++){
		  for(j=0; j<8; j++){
			  x[i][j]=0;
			  x[i][j]=b[i][j]+c[i][j];
		  }
	}

	 for(i=0; i<8; i++){
		  for(j=0; j<8; j++){
			   y[i][j]=0;
			   for (k = 0; k<4; k++) {
				y[i][j]+=a[i][k]*x[k][j];
				}
		  }
	 }

	printf("(i) Matrix A(B+C)=AB+AC : \n");
	printf("Matrix A(B+C) : \n");
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", y[i][j]);
		}
		printf("\n");
	}

/* AB+AC */

	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			ab[i][j]=0;
			ac[i][j]=0;
			for (k = 0; k < 4; k++) {
				ab[i][j]+=a[i][k]*b[k][j];
				ac[i][j]+=a[i][k]*c[k][j];
           		 }
		z[i][j]=ab[i][j]+ac[i][j];
		}
	}

	printf("Matrix AC+BC: \n");
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", z[i][j]);
		}
		printf("\n");
	}

/* (ii)AC=CA */

	printf("(ii) Matrix AC=CA?: \n");
	printf("Matrix AC: \n");
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", ac[i][j]);
		}
		printf("\n");
	}

/* matrix CA */

	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			ca[i][j]=0;
			for (k = 0; k<8; k++) {
				ca[i][j]+=c[i][k]*a[k][j];
           		 }
		}
	}

	printf("Matrix CA: \n");
	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			printf(" %7.4f", ca[i][j]);
		}
		printf("\n");
	}

/* (BA)D */

	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			ba[i][j]=0;
			for (k = 0; k<8; k++) {
				ba[i][j]+=b[i][k]*a[k][j];
         		}
		}
	}

	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			badd[i][j]=0;
			for (k = 0; k<4; k++) {
				badd[i][j]+=ba[i][k]*d[k][j];
        		}
		}
	}

	printf("(iii) Matrix (BA)D=B(AD) : \n");
	printf("Matrix (BA)D : \n");
	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			printf(" %7.4f", badd[i][j]);
		}
		printf("\n");
	}

/* B(AD) */

	for(i=0; i<8; i++){
		for(j=0; j<4; j++){
			ad[i][j]=0;
			for (k = 0; k<4; k++) {
				ad[i][j]+=a[i][k]*d[k][j];
        		}
		}
	}

	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			bbad[i][j]=0;
			for (k = 0; k<8; k++) {
				bbad[i][j]+=b[i][k]*ad[k][j];
        		}
		}
	}

	printf("Matrix B(AD) : \n");
	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			printf(" %7.4f", bbad[i][j]);
		}
		printf("\n");
	}

/* (AB)t */

	for(i = 0; i < 8; i ++){
		for(j = i; j<8 ; j ++){
			abt[i][j]=0;
			abt[j][i]=ab[i][j];
			abt[i][j]=ab[j][i];
		}
	}

	printf("(iv) Transpose Matrices (AB)t and (CA)t : \n");
	printf("Matrix AB : \n");
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", ab[i][j]);
		}
		printf("\n");
	}

	printf("Matrix (AB)t : \n");
	for(i=0; i<8; i++){
		for(j=0; j<8; j++){
			printf(" %7.4f", abt[i][j]);
		}
		printf("\n");
	}

/* (CA)t */

	for(i = 0; i<4; i ++){
		for(j = i; j<4 ; j ++){
			cat[i][j]=0;
			cat[j][i]=ca[i][j];
			cat[i][j]=ca[j][i];

		}
	}

	printf("Matrix CA : \n");
	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			printf(" %7.4f", ca[i][j]);
		}
		printf("\n");
	}

	printf("Matrix (CA)t : \n");
	for(i=0; i<4; i++){
		for(j=0; j<4; j++){
			printf(" %7.4f", cat[i][j]);
		}
		printf("\n");
	}

	return 0;
}

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Solutions
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(i) Matrix A(B+C)=AB+AC :
Matrix A(B+C) :
  1.0810  1.0162  1.3265  0.7034  1.1945  1.3028  1.0937  1.3188
  2.6674  2.6555  3.6139  2.6725  3.4217  3.0126  2.0469  3.3370
  0.3810  0.4354  0.4429  0.3664  0.5665  0.2759  0.3568  0.5105
  2.3290  2.3630  3.1182  2.3581  3.0587  2.5171  1.8071  2.9403
  2.0156  1.7329  2.4823  2.0593  2.7333  2.0591  1.4263  2.3735
  3.1575  3.1351  4.1460  2.8890  3.9550  3.5449  2.6439  3.9468
  0.9480  0.6860  0.9007  0.6306  1.2156  0.8655  0.9013  1.0475
  1.3713  1.4025  1.9227  1.1824  1.5665  1.7570  1.1881  1.7332
Matrix AC+BC:
  1.0810  1.0162  1.3265  0.7034  1.1945  1.3028  1.0937  1.3188
  2.6674  2.6555  3.6139  2.6725  3.4217  3.0126  2.0469  3.3370
  0.3810  0.4354  0.4429  0.3664  0.5665  0.2759  0.3568  0.5105
  2.3290  2.3630  3.1182  2.3581  3.0587  2.5171  1.8071  2.9403
  2.0156  1.7329  2.4823  2.0593  2.7333  2.0591  1.4263  2.3735
  3.1575  3.1351  4.1460  2.8890  3.9550  3.5449  2.6439  3.9468
  0.9480  0.6860  0.9007  0.6306  1.2156  0.8655  0.9013  1.0475
  1.3713  1.4025  1.9227  1.1824  1.5665  1.7570  1.1881  1.7332

(ii) Matrix AC is not equal to CA:
Matrix AC:
  0.8057  0.3472  0.7537  0.3450  0.5303  0.8229  0.3335  0.6587
  1.6288  1.2375  1.7142  1.2613  1.7285  2.0191  0.6416  1.6962
  0.3469  0.1988  0.2170  0.1644  0.3144  0.2049  0.1657  0.3542
  1.4871  1.1101  1.4724  1.1060  1.5713  1.7055  0.6042  1.5606
  1.2135  0.8621  1.0862  0.9234  1.3940  1.3693  0.5380  1.2321
  2.0909  1.3696  2.0587  1.3688  1.9615  2.3514  0.8495  2.0478
  0.7639  0.2497  0.4653  0.2624  0.5759  0.5370  0.3847  0.6002
  0.8489  0.5743  1.0021  0.5869  0.7344  1.1452  0.3038  0.8112
Matrix CA:
  1.8373  1.7247  1.9945  1.7233
  1.7043  1.6497  1.8206  1.8325
  2.1382  2.3264  3.0322  2.8646
  1.1352  1.5557  1.8166  1.7883

(iii) Matrix (BA)D=B(AD) :
Matrix (BA)D :
  1.0002  0.0001  0.0001  0.0000
  0.0001  1.0000  0.0001 -0.0000
  0.0001  0.0000  1.0001  0.0000
  0.0001  0.0001  0.0001  1.0000
Matrix B(AD) :
  1.0002  0.0001  0.0001  0.0000
  0.0001  1.0000  0.0001 -0.0000
  0.0001  0.0000  1.0001  0.0000
  0.0001  0.0001  0.0001  1.0000

It is close to identity matrix I.

(iv) Transpose Matrices (AB)t:
Matrix AB :
  0.2753  0.6690  0.5729  0.3584  0.6642  0.4800  0.7602  0.6601
  1.0386  1.4179  1.8997  1.4112  1.6932  0.9935  1.4052  1.6408
  0.0340  0.2366  0.2259  0.2019  0.2521  0.0710  0.1912  0.1564
  0.8419  1.2530  1.6458  1.2522  1.4874  0.8117  1.2029  1.3797
  0.8021  0.8708  1.3961  1.1360  1.3393  0.6897  0.8882  1.1414
  1.0666  1.7655  2.0873  1.5202  1.9935  1.1935  1.7944  1.8990
  0.1841  0.4363  0.4354  0.3682  0.6397  0.3285  0.5167  0.4473
  0.5224  0.8282  0.9206  0.5955  0.8321  0.6118  0.8843  0.9219
Matrix (AB)t :
  0.2753  1.0386  0.0340  0.8419  0.8021  1.0666  0.1841  0.5224
  0.6690  1.4179  0.2366  1.2530  0.8708  1.7655  0.4363  0.8282
  0.5729  1.8997  0.2259  1.6458  1.3961  2.0873  0.4354  0.9206
  0.3584  1.4112  0.2019  1.2522  1.1360  1.5202  0.3682  0.5955
  0.6642  1.6932  0.2521  1.4874  1.3393  1.9935  0.6397  0.8321
  0.4800  0.9935  0.0710  0.8117  0.6897  1.1935  0.3285  0.6118
  0.7602  1.4052  0.1912  1.2029  0.8882  1.7944  0.5167  0.8843
  0.6601  1.6408  0.1564  1.3797  1.1414  1.8990  0.4473  0.9219