Final answer:
The Israeli army invaded Egypt in 1956 after Egypt nationalized the Suez Canal and closed it to Israeli shipping, leading to the Suez Crisis.
Step-by-step explanation:
The action that led to the Israeli army's invasion of Egypt in 1956 was Egypt's nationalization of the Suez Canal and its subsequent closure to Israeli shipping. On July 26, 1956, President Gamal Abdel Nasser of Egypt announced the nationalization of the Suez Canal, which had been previously controlled by British and French interests. Domestic and international tensions escalated when Nasser closed the canal to Israeli shipping, which was detrimental to Israel's economy and national security.
In response, Israel, along with the United Kingdom and France, planned a military intervention. On October 29, Israel invaded Egypt which led to the Suez Crisis, also known as the Second Arab-Israeli War. This crisis underscored the importance of the Suez Canal to global trade and particularly to European nations that relied on it for access to oil from the Middle East.