How to solve $a^2 = b^2$

Question

It looks pretty simplistic but for me it's a bit complicated >.<.

So this is line one: $a^2 = b^2$

Next we square root both of them. $\sqrt {a^2} = \sqrt {b^2}$

Next move is the part that I'm not sure of. Is it this? $|a| = |b|$ If yes then this?! $\pm a = \pm b$

Please help me.

Answer 1

note that $$a^2 = b^2 \iff a^2-b^2=0\iff (a+b)(a-b) = 0$$

Answer 2

Yes, $\sqrt{x^2}=|x|$ for any real number $x$.

Thus, the equation is equivalent to $|a|=|b|$ and there are two solutions: $a=b$ or $a=-b$.