Question

Prove that \[|a| = |-a|\]

Answer 1

-1 < a < 1 = -1 < -a < 1

=> -1 < a < 1 = 1 > a > -1

Q.E.D

Answer 2

|-a| = |-1| * |a| = 1 * |a| = |a|

Answer 3

abs(a) = a if a>0
=-a if a<0
and abs(-a)=-a if -a>0 this gives a<0
and =-(-a)=aif -a<0 this gives a>0
hence abs(a)=abs(-a)