python3 - <<'EOF'
def det(A):
 n=len(A)
 A=[list(r) for r in A]
 for c in range(n):
  p=next((r for r in range(c,n) if A[r][c]),None)
  if p is None:return 0
  A[c],A[p]=A[p],A[c]
  for r in range(c+1,n):
   if A[r][c]:A[r]=[x^y for x,y in zip(A[r],A[c])]
 return 1
M=[[1 if i==j else 0 for j in range(6)] for i in range(6)]
v=[1]*6
p=0
x=1
one=[sum(M[i])%2 for i in range(6)]
w=[x*v[i]^one[i] for i in range(6)]
C=[[0]*8 for _ in range(8)]
C[0][0]=C[1][1]=1
C[0][1]=C[1][0]=p
for i in range(6):
 C[0][i+2]=C[i+2][0]=v[i]
 C[1][i+2]=C[i+2][1]=w[i]
 for j in range(6):
  C[i+2][j+2]=M[i][j]^(v[i]&v[j])
print('detC',det(C))
D=[[C[i][j]^(i==j) for j in range(8)] for i in range(8)]
print('detCI',det(D))
EOF