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Question
Find A−1 using column transformations:
A = `[(2, -3),(-1, 2)]`
Solution
We know that AA−1 = I
`[(2, -3),(-1, 2)]` A−1 = `[(1, 0),(0, 1)]`
Applying C1 → 2C1 + C2, we get
`[(1, -3),(0, 2)]` A−1 = `[(2, 0),(1, 1)]`
Applying C2 → C2 + 3C1, we get
`[(1, 0),(0, 2)]` A−1 = `[(2, 6),(1, 4)]`
Applying C2 → `(1/2)` C2, we get
`[(1, 0),(0, 1)]` A−1 = `[(2, 3),(1, 2)]`
∴ A−1 = `[(2, 3),(1, 2)]`
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