Exercise · ZW-INVERSE-ELEMENT-008 · ★★☆ Intermediate
Which condition guarantees that a square matrix has an inverse?
Choose one option.
Show answer
- A. Its determinant is nonzero
Explanation
A square matrix has an inverse when its determinant is nonzero. If the determinant is 0 the matrix is singular and has no inverse, and a rectangular matrix has none either.
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-005 If a⁻¹ is the inverse of a, then...
- 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-009 If b is the inverse of a, which equality always holds?