Is the following argument valid?
1. |x| = {x, if x>0; -x, if x<0}; True statement
2. We check both cases:
For x>0, |x|^2= (|x|)^2 = (x)^2 = x^2
For x<0, |x|^2= (|x|)^2 = (-x)^2 = [(-1)^2][(x)^2] = x^2
Thus, |x|^2 and x^2 are interchangeable expressions.