Press and release reset with the board plugged in, and look for a triple-blink pattern. The bootloader only runs after a reset, not at power on, so you won't see a blink from the bootloader if you just apply power, so the test others were recommending above is not conclusive.
(this is true of AVRs with hardware bootloader support, like all official boards and most third party boards based on atmega-series micros; third party boards that don't have hardware bootloader support, but do use a bootloader, like some ATTiny boards, will flash on power on)
I hesitate to do this. But I am a little confused. This seems backwards to what I thought I knew. Not the first time I have been wrong either. 
When I plug my regular Uno's into the USB port to power them they always do the triple blink. When testing clones, the one I have do not triple flash when plugged into a USB port or a 5V wall outlet.
This thread talks about Nano clones.
Strange behaviour on Power up with a Nano Clone.
Posts #7,#8 and #9 in particular.
https://forum.arduino.cc/index.php?topic=540520.msg3684245#msg3684245