Question

Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`

Answer 1

Let A = `[(1, 2),(2, -1)]`

∴ |A| = `|(1, 2),(2, -1)|` = – 1 – 4 = –5 ≠ 0

∴ A^–1 exists.
Consider AA^–1 = I

∴ `[(1, 2),(2, -1)]"A"^-1 = [(1, 0),(0, 1)]`

Appying R₂ → R₂ – 2R₁, we get

`[(1, 2),(0, -5)]"A"^-1 = [(1, 0),(-2, 1)]`

Applying R₂ → `(-1/5)`R₂, we get

`[(1, 2),(0, 1)]"A"^-1 = [(1, 0),(2/5, (-1)/5)]`

Appying R₁ → R₁ – 2R₂, we get

`[(1, 0),(0, 1)]"A"^-1 = [(1/5, 2/5),(2/5, -1/5)]`

∴ A^–1 = `(1)/(5)[(1, 2),(2, -1)]`