Preheat oven to 350 degrees F (175 degrees C). Grease one 8x4 inch loaf pan and set aside.
In a large bowl, sift together the flour, baking powder, and salt. Set aside.
In another bowl, mash the bananas and stir in the eggs and sugar. Stir in the flour mixture and mix until just combined, then fold in the chopped nuts (optional). Pour the batter into the prepared pan.
Bake at 350 degrees F (175 degrees C) for 55 to 65 minutes or until bread tests done. Remove from oven and cool on a rack for 10 minute, then remove from pan and cool completely. Slice and serve.