Exercise · ZW-INVERSE-ELEMENT-005 · ★☆☆ Basic
If a⁻¹ is the inverse of a, then...
Choose one option.
Show answer
- D. a ∗ a⁻¹ = e
Explanation
The inverse of a satisfies a ∗ a⁻¹ = e (and also a⁻¹ ∗ a = e). The option with "+ = 0" only describes the additive case, not the general one.
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.
\[a\ast a^{-1}=a^{-1}\ast a=e\]
More practice problems: inverse element
- ZW-INVERSE-ELEMENT-001 What is the inverse of 5 in (ℤ, +)?
- ZW-INVERSE-ELEMENT-002 What is the inverse of 3/4 under multiplication?
- ZW-INVERSE-ELEMENT-003 In a group, the inverse of an element is...
- ZW-INVERSE-ELEMENT-004 Which identity is correct?
- ZW-INVERSE-ELEMENT-006 The additive inverse of -5 is...
- ZW-INVERSE-ELEMENT-007 Which statement correctly describes the inverse of an element of a group?
- ZW-INVERSE-ELEMENT-008 Which condition guarantees that a square matrix has an inverse?
- ZW-INVERSE-ELEMENT-009 If b is the inverse of a, which equality always holds?