Question

Prove that |a| = |-a|

Answer 1

\[|-a|=\sqrt{(-a)^2}=\sqrt{a^2}=|a|\]

Answer 2

we finally got to apply that square root trick :-D

Answer 3

yeah, I'm not sure how solid of a proof that makes for, but I'm happy with it.

Answer 4

i think there might be a more sophisticated proof but i can't remember

Answer 5

if you do please let me know

Answer 6

There is one:

If \( a \geq 0\), then \(|a| = a = -(-a) = |-a| \), since \( -a \leq 0 \)