Iwo Jima and Okinawa are tiny islands. Why did Japan and the Allies fight for them? (No links or keyboard spam please)

Winning the Battle of Okinawa put Allied forces within striking distance of Japan. On April 1, 1945, the 10th Army, under Lieutenant General Simon Bolivar Buckner, launched the invasion of Okinawa, a strategic Pacific island located midway between Japan and Formosa. Possession of Okinawa would give the United States a base large enough for an invasion of the Japanese home islands.

The Battle of Iwo Jima was an epic military campaign between U.S. Marines and the Imperial Army of Japan in early 1945. Located 750 miles off the coast of Japan, the island of Iwo Jima had three airfields that could serve as a staging facility for a potential invasion of mainland Japan. The island of Iwo Jima was a strategic location because the US needed a place for fighter planes and bombers to land and take off when attacking Japan

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the answer is false.