There are several ways to do it:

The simple Way: a sentinel variable

n = L[0][0]
m = len(A)
found = False
for i in range(m):
   if found:
      break
   for j in range(m):
     if L[i][j] != n: 
       found = True
       break

Pros: easy to understand Cons: additional conditional statement for every loop

The hacky Way: raising an exception

n = L[0][0]
m = len(A)

try:
  for x in range(3):
    for z in range(3):
     if L[i][j] != n: 
       raise StopIteration
except StopIteration:
   pass

Pros: very straightforward Cons: you use Exception outside of their semantic

The clean Way: make a function

def is_different_value(l, elem, size):
  for x in range(size):
    for z in range(size):
     if l[i][j] != elem: 
       return True
  return False
   
if is_different_value(L, L[0][0], len(A)):
  print "Doh"

pros: much cleaner and still efficient cons: yet feels like C

The pythonic way: use iteration as it should be

def is_different_value(iterable):
  first = iterable[0][0]
  for l in iterable:
    for elem in l:
       if elem != first: 
          return True
  return False
   
if is_different_value(L):
  print "Doh"

pros: still clean and efficient cons: you reinvdent the wheel

The guru way: use any():

def is_different_value(iterable):
  first = iterable[0][0]
  return any(cell != first for col in iterable for cell in col)

if is_different_value(L):
  print "Doh"

pros: you'll feel empowered with dark powers cons: people that will read you code may start to dislike you