Let a,b two positive real number...................help

let a,b two positive real number, then a♥b is a positive real number defined in terms of a and b by some fixed rule. suppose the operation a♥b satisfies the equations (a.b)♥b=a(b♥b) and (a♥1)♥a = a♥1, for all a,b >0 if 1♥1 = 1, compute value 19♥98?

I'll use # instead of the heart.

Since (ab)#b = a(b#b) and (1#1) = 1, letting b=1 gives
...a#1 = a(1#1) = a

Since (a#1)#a = a#1, we get
...a#a = a, so b#b = b

The first equation is then
...(ab)#b = a(b#b) = ab

Replace a with c/b for some positive real number c (for each a such a c exists) to get
...(cb/b)#b = c#b = cb/b = c

The operation is entirely determined, then, via a#b = a. The answer is then simply 19.

difficult .. ll take some time..

r u sure about the question.

pl check once..