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There is a famous book/movie, "Run Silent, Run Deep", which involves a submarine duel based loosely on real events.
Submarines can and will hunt and kill each other. In WWII torpedoes did not have active seekers, but relied on contact fusing, which means you would have to set the depth of the torpedo and make a direct hit. This would be very difficult to do because the other sub is a much smaller target than a ship. Nevertheless, in specialized scenarios it is possible. For example, if you are directly following an enemy sub and right behind him, you can load up and just wait for him to turn, then fire, he is 95% dead, even with no active homing.
The main reason this almost never happened in WW2 is because in that war submarines neither were designed to attack each other, or had that as their mission. They were designed as ship killers only, and that is what they did. Run Silent, Run Deep only occurred because the Japanese had specially tasked one of their subs to hunt American subs in a limited, high-importance area. Because of that special mission, a sub duel was likely.