Inverse Matrix
The inverse of matrix A = [[2, 3], [1, 2]] is
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About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- inverse matrix
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
[[2, -3], [-1, 2]]
- Determinant Calculation: ∣A∣=(2)(2)−(3)(1)=4−3=1.
- Adjoint Method: For a 2×2 matrix [acbd], the adjoint is [d−c−ba].
- Swap main diagonal: (2,2)→(2,2)
- Negate off-diagonal: (3,1)→(−3,−1)
- Adjoint Result: adj(A)=[2−1−32].
- Apply Inverse Formula: A−1=∣A∣1adj(A)=11[2−1−32].
This medium 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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