The function f is such that
$$\mathrm { f } ( m n ) = \begin{cases} \mathrm { f } ( m ) \mathrm { f } ( n ) & \text { if } m n \text { is a multiple of } 3 \\ m n & \text { if } m n \text { is not a multiple of } 3 \end{cases}$$
for all positive integers $m$ and $n$.
Given that $\mathrm { f } ( 9 ) + \mathrm { f } ( 16 ) - \mathrm { f } ( 24 ) = 0$, what is the value of $\mathrm { f } ( 3 )$ ?
A $\frac { 8 } { 3 }$
B $2 \sqrt { 2 }$
C 3
D $\frac { 16 } { 5 }$
E $3 \sqrt { 2 }$
F 4