#include <stdio.h>
 #include <math.h>

 #define M 3
 #define N 3

 void inputdata(FILE *fdata, double x[][N],int m, int n);
 void matsum(double x[][N], double y[][N], double z[][N], int m, int n);
 void matprod(double x[][M], double y[][N], double z[][N], int m, int k, int n);
 
 void out_res(FILE *fout, double a[][N], int m, int n);

 int main(void) {

   double a[3][N], b[3][N], c[2][N];
   double sum1[3][N], prod1[3][N];
   FILE   *fdata, *fout;

   fdata = fopen("matrix.txt","r");
   fout  = fopen("output.txt","w");

   inputdata(fdata, a, 3, 2);
   inputdata(fdata, b, 3, 2);
   inputdata(fdata, c, 2, 3);

   matsum(a, b, sum1, 3, 2);
   matprod(a, c, prod1, 3, 2, 3);
   

   printf("A+B =\n");
   fprintf(fout, "A+B =\n");
   out_res(fout, sum1, 3, 2);
   printf("\nA*c =\n");
   fprintf(fout, "\nA*c =\n");
   out_res(fout, prod1, 3, 3);
  
   fclose(fdata);
   fclose(fout);

   return 0;
 }

 void inputdata(FILE *fdata, double x[][N], int m, int n) {

   int    i,j;
   double d;

   for (i = 0; i <= m-1; i++) {
     for (j = 0; j <= n-1; j++) {
       fscanf(fdata, "%lf", &d);
       x[i][j] = d;
     }
   }
 }

 void matsum(double x[][N], double y[][N], double z[][N], int m, int n) {

   int i,j;

   for (i = 0; i <=m-1; i++) {
     for (j = 0; j <=n-1; j++) {
         z[i][j] = x[i][j]+y[i][j];
     }
   }
 }

 void matprod(double x[][M], double y[][N], double z[][N], int m, int k, int n) 
{

   int    i, j, r;
   double a;

   for (i = 0; i <= m-1; i++) {
     for (j = 0; j <= n-1; j++) {
       a = 0;
       for (r = 0; r <=k-1; r++) {
         a = a+x[i][r]*y[r][j];
       }
       z[i][j]=a;
     }
   }
 }

 
 

 void out_res(FILE *fout, double x[][N], int m, int n) {

   int i,j;

   for (i = 0; i <= m-1; i++) {
     for (j = 0; j <= n-1; j++) {
       printf(" %10.3f ", x[i][j]);
       fprintf(fout, " %10.3f ", x[i][j]);
     }
     printf("\n");
     fprintf(fout, "\n");
   }
 }

題名が不適切です。「行列演算」とでも書けばよいものを。

さて、double a[3][2]; と書く代わりに、
int m = 3, n = 2; doulbe *a = malloc(sizeof(double) * m * n);

a[i][j] の代わりに、a[i*n + j] と書くだけで済んでしまうようですが。