Inverse Matrix
If A is an invertible matrix, then (A⁻¹)⁻¹ equals
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About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- inverse matrix
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
A
- Concept: The inverse operation undoes itself.
- Formal Logic: Let B=A−1. By definition of an inverse, B⋅A=I and A⋅B=I. This second equation (A⋅B=I) establishes that A is the inverse of B.
- Substitution: Replacing B with A−1, we find that the inverse of A−1 is A.
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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