If you do the matrix power more cunningly, you don't need to memoize anything. Just use this:

  def mat_pow(m, e):
    if e == 1:
      return m
    else:
      m2 = mat_pow(m, e/2)
      if (e % 1) == 0:
        return m2 * m2
       else:
        return m2 * m2 * m