Consider the following statements regarding the network shown in the figure, $5.184.$ 

(1) The equivalent resistance of the network between points $A$ and $B$ is independent of value of $G$.

(2) The equivalent resistance of the network between point $A$ and $B$ in Fig.$5.184.$ is $\frac{4}{3}R.$ 

(3) The current through $G$ is zero which of the above statement is true