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Question
If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = ______
Options
A
A2
A3
A4
MCQ
Fill in the Blanks
Solution
If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = A3
Explanation:
`|A| = |(3, -3, 4), (2, -3, 4), (0, -1, 1)| = 1 ≠ 0`
adj A = `[(1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`
∴ `A^-1 = [(1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`
`A^2 = [(3, -4, 4), (0, -1, 0), (-2, 2, -3)]`
`A^3 = A^2. A = [(1, -1, 0), (-2, 3, -4), (-2, 3, -3)] = A^-1`
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