Question

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)]`.

Answer 1

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)]`