DS princeton - pls clarify the off. explanation

[arunmmw]

I couldnt understand the explanation provided. My understanding is when X=Y then XY = X^2,

[simplyjat]

That is the intentional gotcha here...

Statement 1 says xy = y^2. and you interpreted it as x = y and this particular interpretation is wrong. xy = y^2 can be true even when y = 0 and in that case x may not be equal to y

[imranme318]

XY=Y^2 ===>XY=Y*Y or -Y*-Y so X=+-Y

X^2=Y^2===>+-X=+-Y ....So Both statements are required here to answer....!

[Ian Stewart]

XY=Y^2 ===>XY=Y*Y or -Y*-Y so X=+-Y

X^2=Y^2===>+-X=+-Y ....So Both statements are required here to answer....!

This isn't right. If x*y = y*y, then we can divide by y if y is not zero. In that case x=y; otherwise y=0. There is no reason to concern yourself with the possibility that x = -y; that will *not* be true except when x=0 *and* y=0.