Well this is kind of hard to answer but it should be zero because if the identity property of addition would be the same answer. Here let me give you an example: 8+0=8, 125+0=125 so identity property of zero should be zero. 0+0=0
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The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.
There are many properties of multiplication. There is the associative property, identity property and the commutative property. There is also the zero product property.
If you add zero to a number, the number will stay the same.
Zero is the identity under addition.
Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0 * a [distributivity of multiplication over addition] 0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse] 0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses] 0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition] 0 = 0 * a + 0 [property of additive inverses] 0 = 0 * a [additive identity] A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).