Rn41 Bluetooth Module Does Not Respond

I want to send some commands to my RN41 Bluetooth Module connecting to Arduino Leonardo over the serial port using serial monitor, as the tutorial shows. But it does not respond. I can connect to the bluetooth modul and the status LED blinks right. I tried to send $$$ to change to command mode, and the blink rate does change to 10/sec, but module responds nothing. And when I send '---', the blink rate back to normal. I think it means the connection is successful but I just cannot see anything at serial monitor.
I set monitor's baud to 9600, as exactly the tutorial shows. (Using the BlueSMiRF - SparkFun Learn)
Do you guys know what could be wrong?
Code attached:
/*
Example Bluetooth Serial Passthrough Sketch
by: Jim Lindblom
SparkFun Electronics
date: February 26, 2013
license: Public domain

This example sketch converts an RN-42 bluetooth module to
communicate at 9600 bps (from 115200), and passes any serial
data between Serial Monitor and bluetooth module.
*/
#include <SoftwareSerial.h>

int bluetoothTx = 2; // TX-O pin of bluetooth mate, Arduino D2
int bluetoothRx = 3; // RX-I pin of bluetooth mate, Arduino D3

SoftwareSerial bluetooth(bluetoothTx, bluetoothRx);

void setup()
{
Serial.begin(9600); // Begin the serial monitor at 9600bps

bluetooth.begin(115200); // The Bluetooth Mate defaults to 115200bps
bluetooth.print("$"); // Print three times individually
bluetooth.print("$");
bluetooth.print("$"); // Enter command mode
delay(100); // Short delay, wait for the Mate to send back CMD
bluetooth.println("U,9600,N"); // Temporarily Change the baudrate to 9600, no parity
// 115200 can be too fast at times for NewSoftSerial to relay the data reliably
bluetooth.begin(9600); // Start bluetooth serial at 9600
}

void loop()
{
if(bluetooth.available()) // If the bluetooth sent any characters
{
// Send any characters the bluetooth prints to the serial monitor
Serial.print((char)bluetooth.read());
}
if(Serial.available()) // If stuff was typed in the serial monitor
{
// Send any characters the Serial monitor prints to the bluetooth
bluetooth.print((char)Serial.read());
}
// and loop forever and ever!
}