I'm having a really hard time understanding this.

The MLE of a function of a parameter is the function of the MLE of the parameter.

That is if and is the MLE of , then the MLE of is

Ok, so the MLE of a function of a parameter is the same function with the MLE of the parameter fed into it. That's my understanding.

But the next claim is that for any square of a parameter the MLE of the square of the parameter will be the square of the MLE of the parameter. I just can't see how this follows.