Why did the Japanese occupation invade Singapore?

Japan's motivation for the invasion of Singapore was primarily strategic and economic. Being an island nation lacking in natural resources, Japan was looking for long-term solutions to a chronic problem that left them vulnerable and beholden to larger, resource-rich Imperialistic nations. They set their sights on their nearest neighbor: China, whom they viewed as weak and vulnerable after centuries of Imperialistic victimization.
Early expansion into northern China throughout the second half of the 1930's yielded surprising success. It was only when they began to threaten foreign holdings to the south, that the Western powers started to push back in earnest.
With trade embargos levied against them by Britain and the U.S., Japan's ruling militarist regime decided to neutralize the most prominent threats in a simultaneous attack on areas of Southeast Asia and the Pacific theater from which Allied powers could launch strikes that would impede Japanese plans to control the region.
It was necessary to take Singapore, nicknamed the 'Gibraltar of the East', because it was home to a major British military base that oversaw the defense of British holdings in Southeast Asia. With all major ports and strongholds throughout the region in Japanese hands, and the U.S. navy all but destroyed at Pearl Harbor, Western powers would be hard pressed to stop Japan from achieving its goal: the seizure and control of China's vast resources.

Imperial Japan was very much a martial society, one in which the armed forces enjoyed a high level of prestige and influence. Combined with an intense nationalism, the militarization of Japanese life had turned the country into an aggressive power, willing and able to wage war. All of the available evidence suggests that the Japanese had been preparing for war in South East Asia since at least 1936. Yet it took the outbreak of World War II in Europe for the Japanese high command to put its long-standing military strategy into effect.
Large parts of South East Asia belonged to European imperial powers, mainly Great Britain and France. Emboldened by its successes in Manchuria, the Japanese invaded British colonial territories, such as Hong Kong and Singapore. Singapore was known as "The Gibraltar of the East" and was a key strategic stronghold in the British Empire. As the Japanese were set on establishing an empire of their own, it made sense from a strategic standpoint to occupy this part of East Asia.
The British were unable to put up much resistance to the Japanese, as they were bogged down in fighting the Germans in Europe and so were dangerously overstretched in relation to defending their empire. The Japanese were also able to take advantage of the weakness of a defeated France to invade and occupy French Indochina.