ANY number/value multip.ied to zero(0) = zero(0)
2 x 0 = 0
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The zero property of multiplication is that for any number multiplied by zero, the product is zero.
For example:
0x0=0
0x1=0
0x2=0
0x3=0
The multiplicative property of zero states that any number multiplied by zero will equal zero.
A x 0 = 0
The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.
zero property
Why am I wasting my time with such an obvious question? Multiplication Property of Zero! If you multiply anything by zero, the product is zero!
Equals divided by non-zero equals are equal.
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).