Question

If A = `[(8, -4),(-5, 3)]`, verify that A(adj A) = (adj A)A = |A|I₂ 

Answer 1

A = `[(8, -4),(-5, 3)]`

|A| = 24 – 20 = 4 ≠ 0.A^–1 ecists.

adj A = `[(3, 4),(5, 8)]`

A(adj A) = `[(8, -4),(-5, 3)][(3, 4),(5, 8)]`

= `[(24 - 20, 32 - 32),(-15 + 15, -20 + 24)]`

= `[(4, 0),(0, 4)]`  ........(1)

(adj A)A = `[(3, 4),(5, 8)][(8, -4),(-5, 3)]`

= `[(24 - 20, -12 + 12),(-40 + 40, -20 + 24)]`

= `[(4, 0),(0, 4)]`   ........(2)

|A|I₂ = `4[(1, 0),(0, 1)]`

= `[(4, 0),(0, 4)]`  ........(3)

 (1), (2) and (3)

⇒ A(adj A) = (adj A)A = |A|I₂