Question 69
Given any two positive real numbers $x$ and $y$, then $x \diamond y$ is a positive real number defined in terms of $x$ and $y$ by some fixed rule. Suppose the operation $x \diamond y$ satisfies the equations $(x \cdot y) \diamond y = x(y \diamond y)$ and $(x \diamond 1) \diamond x = x \diamond 1$ for all $x, y \gt 0$. Given that $1 \diamond 1 = 1$, find $19 \diamond 98$.