Bananas will rot faster and turn brown faster in the refrigerator mainly due to the formation of ice crystals when they are refrigerated.
It's best to keep bananas out on the counter or in the pantry to keep them from rotting too fast.
Bananas will last between 5 to 7 days out on the counter or in the pantry at room temperature although they are still safe to eat when the bananas are turning brown.
Even when bananas are turning brown a bit and getting more ripe the bananas are still safe to eat.
But it's best to eat the bananas within a week of buying them.
Putting the bananas in the refrigerator really is not a good idea because the bananas will rot faster in the refrigerator.