3x3 matrix determinant cofactor inverse

#include <math.h>
#include <stdio.h>
#define M 3
static void print_matrix(const double a[][M]) {
  for (int i = 0; i < M; ++i) {
    for (int j = 0; j < M; ++j) { printf("%f\t", a[i][j]); }
    puts("");
  }
}
static double determinant(const double a[][M]) {
  double D = 0.;
  for (int i = 0; i < M; i++) {
    D += a[0][i] * (a[1][(i + 1) % 3] * a[2][(i + 2) % 3] -
                    a[1][(i + 2) % 3] * a[2][(i + 1) % 3]);
  }
  return D;
}
static void cofactor(const double a[][M], double b[][M]) {
  for (int i = 0; i < M; i++) {
    for (int j = 0; j < M; j++) {
      b[i][j] = a[(i + 1) % 3][(j + 1) % 3] * a[(i + 2) % 3][(j + 2) % 3] -
                a[(i + 1) % 3][(j + 2) % 3] * a[(i + 2) % 3][(j + 1) % 3];
    }
  }
}
static void inverse(const double a[][M], double b[][M]) {
  double det = determinant(a);
  cofactor(a, b);
  for (int i = 0; i < M; ++i) {
    for (int j = 0; j < M; ++j) {
      if (j < i) {
        continue;
      } else if (i == j) {
        b[i][i] /= det;
        continue;
      }
      double t = b[i][j];
      b[i][j] = b[j][i] / det, b[j][i] = t / det;
    }
  }
}
static void multi(const double a[][M], const double b[][M], double c[][M]) {
  for (int i = 0; i < M; ++i) {
    for (int j = 0; j < M; ++j) {
      double s = 0.;
      for (int k = 0; k < M; ++k) { s += a[i][k] * b[k][j]; }
      c[i][j] = s;
    }
  }
}
int main(void) {
  double a[M][M] = {{4.0, 1.0, -5.0}, {3.0, -2.0, 1.0}, {5.0, 3.0, -5.0}};
  printf("A =\n"), print_matrix(a);
  printf("det(A) = %f\n", determinant(a));
  double b[M][M] = {0};
  cofactor(a, b), printf("cofactor(A) =\n"), print_matrix(b);
  inverse(a, b), printf("inverse(A) =\n"), print_matrix(b);
  double c[M][M] = {0};
  multi(a, b, c), printf("check. A * inverse(A) =\n"), print_matrix(c);
}