abstract algebra – Algebraic property dominated for 1 $ times 0 = 0 $?

It is well known that each number multiplied by $ 0 is $ 0 and each number multiplied by $ 1 $ is the number itself, now I'm confused to get the answer convinced to this question, Is that $ 1 times 0 = 0 $ is the result of the first property "each number multiplied by $ 0 is $ 0 or a result of the second property each number multiplied by $ 1 $ is the number itself?