Bluetooth RN41 does not respond - arduino

Question

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. (https://learn.sparkfun.com/tutorials/using-the-bluesmirf/example-code-using-command-mode)
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!
}

Answer 1

I was stuck on very simple case:
To enter command mode you have to send $$$ without any CR/LF.
after you entered command mode you have to send commands, and every command has to be followed by CR LF. if not - module will not response.
Hope that helps.

Answer 2

Yes, send only 3 characters, "$$$". I was also stuck for a bit. I also found that reading the Mate response "CMD" is necessary, which is not shown in the published sketch.

Answer 3

I've got some brandnew RN41VX modules.
I connect them by a XBEE Explorer USB module (almost same as RN41 EVAL Kit) to computer.
Using a terminal with 115 kbaud I send $$$ (without any trailing chars as 0x0d) to get into command mode. The LED switches to 10Hz blinhking - all fine.
But no respone appears in terminal.
Solution:
I had to switch on RTS Signal, even if manual tells "Flow Control: none"
kind regards Volker