Order in which to take max and square

Question

I am pretty sure that $(\displaystyle\max_i\{|a_i|\})^2=\max_i\{|a_i|^2\}$ where $i=1,\ldots, n$ and $a_i\in\mathbb{R^n}$. Could someone please confirm?

Answer 1

Yes, this is because $x \mapsto x^2$ is an increasing function for $x > 0$.