Can you explain Inverse Axiom (Both addition and multiplication)? Can anyone explain this in a "PROOFING" manner? ... (see below)

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Can you explain Inverse Axiom (Both addition and multiplication)? Can anyone explain this in a "PROOFING" manner? ... (see below)

Mathematics
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Is this true? Explain why. \[4(\frac{ 1 }{ 4 }) = 1\]
Do you know what multiplication inverse is?
reciprocal

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Other answers:

A number multiplied by its reciprocal is always equal to 1.
"A number which is, 4, multiplied by its reciprocal, 1/4, is equal to 1." Is that how your write in proofing?
\[a \cdot a^{-1}=1 \text{ for all } a \neq 0\] This is just the multiplicative inverse property
Ok so what axiom system your working on ??
I'm working on all types of axiom. From the 5 basics of axiom of equality to the other axioms. I'm just wondering on how could explain it. I saw this material in the internet: http://www.mathhands.com/046/hw/046c01s06ns.pdf Under the "Some questions to think about". Do you have any idea how to explain it in a way the author wants it to be?
In addition to that question, I can't seem to find any other explanation or differences between the 5 basic axioms of Algebra ( Reflexive, Symmetric, Transitive, Additive, and Multiplicative.
so I guess you are looking for something more then "example: 1/3 is the multiplicative inverse of 3 so 1/3*3=1 or 3*1/3=1" ?
So if the Prof asked me, "True, False, WDKY (we don’t know yet)) \[3(\frac{ 1 }{ 3 }) =3\] Do you know why? exp lain." How will I form my answer?
that would be false because 3*1/3=1
we already mentioned the multiplicative inverse property above \[a \neq 0\] \[a (\frac{1}{a})=1 \text{ since } a \text{ and } \frac{1}{a} \text{ are multplicative inverses of each other }\]
I don't know what other answer you are looking for honestly
Maybe, I was expecting a complicated explanation. T.T If it's that simple, then okay. Thank you very much.

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