Question

If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`

Answer 1

BA = `[(4, 1),(2, 3),(1, 2)]_(3 xx 2)  [(2, 1, 2),(1, 2, 4)]_(2 xx 3)`

BA = `[(8 + 1, 4 + 2, 8 + 4),(4 + 3, 2 + 6, 4 + 12),(2 + 2, 1 + 4, 2 + 8)]_(3 xx 3)`

= `[(9, 6, 12),(7, 8, 16),(4, 5, 10)]_(3 xx 3)`

Now AB = `[(2, 1, 2),(1, 2, 4)]_(2 xx 3) [(4, 1),(2, 3),(1, 2)]_(3 xx 2)`

= `[(8 + 2 + 2, 2 + 3 + 4),(4 + 4 + 4, 1 + 6 + 8)]_(2 xx 2)`

= `[(12, 9),(12, 15)]_(2 xx 2)`

Hence, BA = `[(9, 6, 12),(7, 8, 16),(4, 5, 10)]` and AB = `[(12, 9),(12, 15)]`.