Exercise · ZW-INVERSE-ELEMENT-001 · ★☆☆ Basic
What is the inverse of 5 in (ℤ, +)?
Choose one option.
Show answer
- D. −5
Explanation
The inverse of 5 in (ℤ, +) is −5, because 5 + (−5) = 0, which is the identity. 1/5 would be the multiplicative inverse and is not an integer.
Review the concept: Inverse element
Given \(a\in G\), an element \(b\in G\) is an inverse of \(a\) if operating in both orders gives the neutral element.
\[a\ast a^{-1}=a^{-1}\ast a=e\]
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