This statement is false. If aggregate expenditures rise unexpectedly (and aggregate production does not rise to accompany it) inventories will actually drop rather than rising.
The term “aggregate expenditures” refers to the amount of goods that is bought in the economy. The term “aggregate production” refers to the amount of goods that is produced. When the economy is in equilibrium, these two numbers are the same. People are willing to buy exactly as much as the producers make.
But now imagine that aggregate expenditures rise unexpectedly. We know that this means that people are buying more than expected. If people buy more than is expected, will inventories rise? No, they will not. Instead, they will fall because stores and other sellers will not have as much in their storerooms and warehouses. People will be buying more than expected so inventories will drop. This means that the statement is false.