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## Why is subtraction anticommutative? – All of the useful answers

Explore Why is subtraction anticommutative? with tags: *Subtraction wikipedia, Subtraction operation, Commutator properties, Cross product, Lie algebra, What is an algebra, Properties of anticommutators, Math operations*

## The best fruitful answer to Why is subtraction anticommutative?

### Subtraction on Numbers is Anticommutative – ProofWiki

**Summary:***Subtraction on Numbers is Anticommutative Theorem The operation of subtraction on the numbers is anticommutative. That is: $a – b = b – a \iff a = b$ Proof Natural Numbers $a – b$ is defined on $\N$ only if $a \ge b$. If $a > b$, then although $a – b$ is defined, $b – a$ is not. So…***Author:**proofwiki.org**Rating:**3.97 ⭐**Source:**https://proofwiki.org/wiki/Subtraction_on_Numbers_is_Anticommutative

### Anticommutative property – Hellenica World

**Summary:***Anticommutative property In mathematics, anticommutativity is a specific property of some non-commutative operations. In mathematical physics, where symmetry is of central importance, these operations are mostly called antisymmetric operations, and are extended in an associative setting to cover more than two arguments. Swapping the position of two arguments of an antisymmetric operation yields a result, which is the inverse of the result with unswapped arguments. The notion inverse refers to…***Author:**hellenicaworld.com**Rating:**4.42 ⭐**Source:**https://www.hellenicaworld.com/Science/Mathematics/en/Anticommutativeproperty.html

### Does this property of subtraction and division have a name?

**Summary:***Does this property of subtraction and division have a name? A helpful way to rewrite that statement would be (assuming subtraction for simplicity): $x – y – z ⇔ x – z – y$ We are observing how swapping y and z does not change the value of the expression. While it may initially look like there is a useful property behind this, the example is showing…***Author:**matheducators.stackexchange.com**Rating:**3.16 ⭐**Source:**https://matheducators.stackexchange.com/questions/18845/does-this-property-of-subtraction-and-division-have-a-name

data-jsarwt=”1″ data-usg=”AOvVaw34FgFBrcNBWsxSIkmSjhQz” data-ved=”2ahUKEwi0y-GNiOb6AhWcaGwGHTf4BzMQuAJ6BAgKEAU”>8:55Vector subtraction is Anti Commutative … Millions of thanks from depths of My Heart to every subscriber and Viewer. Get a “CHANCE TO APPEAR ON …YouTube · M Asif Physics · 25 ago 2020

### anticommutative – PlanetMath

**Summary:***anticommutative A binary operation “⋆” is said to be anticommutative if it satisfies the identity where the minus denotes the element in the algebra in question. This implies that x⋆x=-(x⋆x), i.e. x⋆x must be the neutral element of the addition of the algebra: Using the distributivity of “⋆” over “+” we see that the indentity (2) also implies (1): 𝟎=(x+y)⋆(x+y)=x⋆x+x⋆y+y⋆x+y⋆y=x⋆y+y⋆x A well known example of anticommutative operations is the vector product in the…***Author:**planetmath.org**Rating:**4.25 ⭐**Source:**https://planetmath.org/anticommutative

### Is matrix subtraction commutative? + Example – Socratic

**Summary:***Is matrix subtraction commutative? + ExampleNo, but it is not too difficult to show that it is anticommutative. For #C = A – B#, looking at the entry on row #i# and column #j#: #c_(ij) = a_(ij) – b_(ij)# Thus: #c_(ij) = -(b_(ij) – a_(ij)) = a_(ij) – b_(ij)# or #C = -(B – A)# which we should expect from knowing that subtraction is itself anticommutative. So, if…***Author:**socratic.org**Rating:**4.8 ⭐**Source:**https://socratic.org/questions/is-matrix-subtraction-commutative