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Questions
Find the inverse of the following matrix.
`[(2, -3),(-1, 2)]`
Find the inverse of matrix A by elementary row transformations, where A = `[(2, -3),(-1, 2)]`
Solution
Let A = `[(2, -3),(-1, 2)]`
∴ |A| = `[(2, -3),(-1, 2)]` = 4 − 3 = 1 ≠ 0
∴ A−1 exists.
Consider AA−1 = I
∴ `[(2, -3),(-1, 2)]`A−1 = `[(1, 0),(0, 1)]`
By R1 + R2, we get,
`[(1, -1),(-1, 2)]`A−1 = `[(1, 1),(0, 1)]`
By R2 + R1, we get,
`[(1, -1),(0, 1)]`A−1 = `[(1, 1),(1, 2)]`
By R1 + R2, we get,
`[(1, 0),(0, 1)]`A−1 = `[(2, 3),(1, 2)]`
∴ A−1 = `[(2, 3),(1, 2)]`
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