Nikon d3100- why won't shutter go any slower than 1/60th in A mode with flash?

When I'm in Aperture priority mode and I want to use about F24 with the flash on, my shutter won't go any slower than 1/60th even though the meter is showing the picture as being very under-exposed. If I have the flash ON OR OFF in Manual or Shutter priority mode the shutter will go slower than 1/60th. It is only if I have my flash OFF in Aperture priority mode the shutter will go slower than 1/60fth. This does not make sense.

Just put it in manual and adjust the shutter speed from there

I got this from Dpreview: • P, A modes: Fill flash, rear-curtain with slow sync, slow sync, slow sync with red-eye reduction, red-eye reduction

That suggests that it will go slower. Check out your owner's manual under flash modes.

How about just using your camera in the manual mode. With it you can have complete control of the aperture and shutter speed.

Maybe because of the flash it (the camera) doesn't think it needs to go lower than 1/60th (but once you turn off the flash, then it knows it needs to go below 1/60th in order to have decent exposure).

try it and see. Are your pictures underexposed?