Inverse Matrix
A matrix A has an inverse if and only if
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About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- inverse matrix
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
|A| ≠ 0
- Singular vs Non-singular: A matrix with determinant equal to zero is called 'Singular' and has no inverse.
- Invertibility Condition: For a matrix A to be invertible, it must be non-singular, meaning ∣A∣=0.
- Reason: The formula for the inverse involves dividing by the determinant: A−1=∣A∣1adj(A). If ∣A∣=0, the expression is undefined.
This easy difficulty mathematics question is from the chapter matrices and determinants, covering the topic of inverse matrix. It appeared in the 2025 exam.
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