What you have done so far is correct (though you have used the wrong implies symbol, you should be using ), but you have only proven the if statement. To prove the iff statement (if and only if) you need to prove it in the other direction as well. I.e. show that if m^2 is divisible by 3, then so is m.
This will be easiest to prove using the contrapositive - i.e. if m is not divisible by 3, then neither is m^2.
This means that or only.
which is not divisible by 3.
Do the same for .