I have seen chapters on automata in my Discrete Math books so I'm hoping this is the right forum for this question

I have a question(2/3 of it answered). I was hoping to have what I've done so far checked and maybe get a hint on how to approach the last part.

For two regular languages.

a. Is LM = ML?

b. Is it true if the alphabet is only {0,1}?

c. Is it true if the alphabet is only {0}?

a. No LM != ML

let M = {abc, acb} L= {bca, bac}

M and L are both finite, therefore M and L are regular languages

ML = {abcbca, abcbac, acbbca, acbbac}

LM = {bcaabc, bcaacb, bacabc, bacacb}

here LM != ML

b. No LM != ML if the alphabet is {0,1}

let L = {0,00}

let M = {1,11}

M and L are both finite, therefore M and L are regular languages

LM = {01,011, 001, 0011}

ML = {10, 100, 110, 1100}

here LM != ML

c. if the alphabet is only {0} I would like to say that LM = ML for all languages M and L

I'm not quite sure how to prove it though. I'm not receiving very much help on how to tackle these problems through the lectures in class so I'm kinda teaching myself.