Can't get XBee S1 with Adafruit adapter going with Arduino Uno R3
I have connected RX on XBee adapter to RX on the Arduino, and TX on XBee adapter to TX on the Arduino (similarly 5V and GND). The Arduino is connected to COM9 on my PC, and the green LED flashes. When I run X-CTU, select COM9 and try a Test/Query, I get an "Unable to communicate with modem" message.
I have another, matching XBee with adapter connected to a Boarduino with FTDI lead to another PC, which seems to work OK. I have swapped around the XBees and adapters, and the same thing happens ie the Arduino Uno end still doesn't work. When I try the Test/Query on the Arduino, the red light on the Boarduino's XBee adapter comes on, so there seems to be some communication between them.
Typing into the Arduino's X-CTU Terminal echoes on the Boarduino's terminal, but not the other way round.
I would be very grateful for your help.