Question

If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)^T = A^TB^T.

Answer 1

BA = `[(0, 3, -4),(2, -1, 1)][(2, -1),(3, -2),(4, 1)]`

= `[(0 + 9 - 16, 0 - 6 - 4),(4 - 3 + 4, -2 + 2 + 1)]`

∴ BA = `[(-7, -10),(5, 1)]`

∴ (BA)^T = `[(-7, 5),(-10, 1)]`          ...(i)

A^TB^T = `[(2, 3, 4),(-1, -2, 1)][(0, 2),(3, - 1),(-4, 1)]`

= `[(0 + 9 - 16, 4 - 3 + 4),(0 - 6 - 4, -2 + 2 + 1)]`

= `[(-7, 5),(-10, 1)]`                ...(ii)
From (i) and (ii)
(BA)^T = A^TB^T.