No, bananas are not a vegetable; they are a fruit.
Bananas fit the botanical definition of a fruit because they develop from the flower of the banana plant and contain the seeds of the plant (though in commercially grown bananas, these seeds are reduced to small specks). Fruits are the mature ovaries of flowering plants, containing seeds. Vegetables, on the other hand, are typically roots, stems, or leaves of plants. Therefore, based on this definition, bananas are correctly classified as fruits.