Question

If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A^-1 by using elementary transformation .

Answer 1

Consider  AA^-1 = I

∴ `[(1,0,0),(2,1,0),(3,3,1)]"A"^-1 = [(1,0,0),(0,1,0),(0,0,1)]`

Apply R₂ → R₂ - 2R₁ , R₃ → R₃ - 3R₁

∴ `[(1,0,0),(0 ,1,0),(0,3,1)]"A"^-1 = [(1,0,0),(-2,1, 0),(-3, 0,1)]`

Apply R₃ → R₃ - 3R₂ 

∴ `[(1,0,0),(0,1,0),(0,0,1)]"A"^-1 = [(1,0, 0),(-2,1,0),(3,-3,1)]`

∴ IA^-1 = `[(1,0,0),(-2,1,0),(3,-3,1)]`

∴ A^-1 = `[(1,0,0),(-2,1,0),(3,-3,1)]`