Stuti Bhawan

Now $$a^2= b^2 \iff (-a)^2 = a^2 = b^2 = (-b)^2 $$

And that's why, $$|a|=|b| \iff |a|=±b$$ but $$|a|=-b $$ is not possible as modulus of any thing cannot be negative. So $$|a| = b$$

$$ \iff ±a=b $$

$$ \text{OR} \ \ \ \ \ a=b , a=-b \ \ \ \ \ \square $$

I would like to give $ \text{ONE MORE} $ proof.

We have, $$|a|=|b|$$

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