Final answer:
Energy flows through ecosystems from producers to consumers, while matter, including elements and water, is recycled within the ecosystem according to the law of conservation of matter and energy.
Step-by-step explanation:
The correct statement regarding how matter and energy are used in ecosystems is that energy flows through ecosystems; matter cycles within and through ecosystems. This is because ecosystems require constant inputs of energy, most commonly from sunlight, to sustain life. Energy flows from this source through producers like plants and then through consumers like animals. In contrast, matter, including crucial elements like carbon and nitrogen as well as water, is recycled within the ecosystem. This matter undergoes countless forms of transformation and movement, but the total amount of matter remains constant, adhering to the law of conservation of matter. Similarly, energy is conserved; it is neither created nor destroyed but simply transferred and transformed.