To find the value of f(9), we need to substitute a = 9 and b = 9 into the given function f(a b) = a f[f(b)].

Substituting a = 9 and b = 9, we get:
f(9 9) = 9 f[f(9)]

Now, let's simplify the expression step by step:

1. f(9 9) = 9 f[f(9)]

2. f(18) = 9 f[f(9)]

3. Since f(9) is still unknown, let's denote it as x:
f(18) = 9 f(x)

4. Now, let's substitute a = 18 and b = 9 into the given function f(a b) = a f[f(b)]:

f(18 9) = 18 f[f(9)]

5. Simplifying further:
f(27) = 18 f[f(9)]

6. Since f(9) is still unknown, let's denote it as x:
f(27) = 18 f(x)

7. Now, let's substitute a = 27 and b = 9 into the given function f(a b) = a f[f(b)]:

f(27 9) = 27 f[f(9)]

8. Simplifying further:
f(36) = 27 f[f(9)]

9. Since f(9) is still unknown, let's denote it as x:
f(36) = 27 f(x)

10. We can see a pattern here:
f(18) = 9 f(x)
f(27) = 18 f(x)
f(36) = 27 f(x)

11. From the pattern, we can observe that f(n) = (n-9) f(x), where n is a positive integer greater than 9.

12. Now, let's substitute n = 9 into the pattern:
f(9) = (9-9) f(x)
f(9) = 0 f(x)

13. Finally, substituting f(9) = 0 into the equation f(36) = 27 f(x):
0 = 27 f(x)

14. Since 27 f(x) equals zero, f(x) must be zero as well.

15. Therefore, f(9) = 0.

Hence, the correct answer is option 'D' - 9.