Are Y=0 and X=0 perpendicular?

Yes, they are perpendicular, but you are mentioning the x and y axes itself in that case, and they intersect at the point of origin.

However, we are not interested in lines having zero slopes, because as you will notice, the rule of " the product of their slopes is negative one , (-1)" can be forfeited. What we can say is, vertical and horizontal lines are undefined, that's why their slopes are zero.

Y = 0 is a horizontal line.
X = 0 is a vertical line.
Lines are perpendicular.

Yes, they are perpendicular, but you are mentioning the x and y axes itself in that case, and they intersect at the point of origin.

Yes, they are perpendicular. The given statement is not exactly true. It only holds when both lines have defined slopes--so that "their product is -1" is meaningful.

A more accurate statement is that two lines are perpendicular if either (a) both have defined slopes and the product of those slopes is -1, or (b) one line as an undefined slope and the other has a slope of 0.