Are the molecular and imperical formula of lauryl alcohol the same? C12 H26 O?

If the formula you wrote is correct, yes. How do I know. Because there is only 1 O atom. For the molecular formula and empirical formula to be different, the molecular formula must be a multiple of the empirical formula. And for that to happen, the molecular formula must be divisible by a whole number; i.e., 2, 3 etc. C12H26O2 would qualify with C6H13O the empirical formula and C12H26O2 the molecular formula.