Question

Verify that A² = I when A = `[(0, 1, -1),(4, -3, 4),(3, -3, 4)]`

Answer 1

We have, A = `[(0, 1, -1),(4, -3, 4),(3, -3, 4)]`

∴ A² = `[(0, 1, -1),(4, -3, 4),(3, -3, 4)] * [(0, 1, -1),(4, -3, 4),(3, -3, 4)]`

= `[(0 + 4 - 3, 0 - 3 + 3, 0 + 4 - 4),(0 - 12 + 12, 4 + 9 - 12, -4 - 12 +16),(0 - 12 + 12, 3 + 9 - 12, -3 - 12 + 16)]`

= `[(1,0, 0),(0, 1, 0),(0, 0, 1)]`

= I

Hence proved.