Question

For any real number a, prove that $a\times 0=0$.

Answer 1

Observe $0+0=0$, by the additive identity property of 0. Using distributive property
$a\times 0=a\times (0+0)=a\times 0+a\times 0$
We can cancel $a\times 0$ on both sides and get $a\times 0=0$.