Question

If A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`, then verify (BA)^T = A^TB^T

Answer 1

A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`

∴ A^T = `[(2, 0, 1),(1, 3, -1)]` and B^T = `[(0, 1),(3, -7),(5, 2)]`

BA = `[(0, 3, 5),(1, -7, 2)][(2, 1),(0, 3),(1, -1)]`

= `[(0 + 0 + 5, 0 + 9 - 5),(2 - 0 + 2, 1 - 21 - 2)]`

∴ BA = `[(5, 4),(4, -22)]`   .....(i)

∴ A^TB^T = `[(2, 0, 1),(1, 3, -1)][(0, 1),(3, -7),(5, 2)]`

= `[(0 + 0 + 5, 2 - 0 + 2),(0 + 9 - 5, 1 -21 - 2)]`

= `[(5, 4),(4, -22)]`   .....(ii)

From (i) and (ii), we get

(BA)^T = A^TB^T