Question

If A = `[(1, 2),(2, 1)] "and B" = [(2, 1),(1, 2)]`, find A(BA).

Answer 1

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

B = `[(2, 1),(1, 2)]`

BA = `[(2, 1),(1, 2)] xx [(1, 2),(2, 1)]`

= `[(2 xx 1 + 1 xx 2, 2 xx 2 + 1 xx 1),(1 xx 1 + 2 xx 2, 1 xx 2 + 2 xx 1)]`

= `[(2 + 2, 4 + 1),(1 + 4, 2 + 2)]`

= `[(4, 5),(5, 4)]`

A(BA) = `[(1, 2),(2, 1)] xx [(4, 5),(5, 4)]`

= `[(1 xx 4 + 2 xx 5, 1 xx 5 + 2 xx 4),(2 xx 4 + 1 xx 5, 2 xx 5 + 1 xx 4)]`

= `[(4 + 10, 5 + 8),(8 + 5, 10 + 4)]`

= `[(14, 13),(13, 14)]`