python3 - <<'EOF'
def inv(C):
 n=len(C)
 A=[row[:] [1 if i==j else 0 for j in range(n)] for i,row in enumerate(C)]
 for c in range(n):
  p=next(r for r in range(c,n) if A[r][c])
  A[c],A[p]=A[p],A[c]
  for r in range(n):
   if r!=c and A[r][c]: A[r]=[x^y for x,y in zip(A[r],A[c])]
 return [row[n:] for row in A]
Cs=[[[1,0,0,1],[0,1,1,0],[0,1,0,1],[1,0,1,0]],[[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]],[[1,1,1,0],[1,1,0,1],[1,0,0,1],[0,1,1,0]]]
for C in Cs:
 I=inv(C)
 d=[C[i][i] for i in range(4)]
 u=[sum(I[i][j]*d[j] for j in range(4))%2 for i in range(4)]
 q=sum(d[i]*u[i] for i in range(4))%2
 print('d',d,'diagI',[I[i][i] for i in range(4)],'u',u,'q',q)
EOF