Question

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (AB)^T = B^TA^T

Answer 1

We have,

A = `[(1, 2),(-1, 3)]`

B = `[(4, 0),(1, 5)]`

C = `[(2, 0),(1, -2)]`

And a = 4, b = –2

AB = `[(1, 2),(-1, 3)] [(4, 0),(1, 5)]`

= `[(4 + 2, 0 + 10),(-4 + 3, 0 + 15)]`

= `[(6, 10),(-1, 15)]`

∴ (AB)^T = `[(6, -1),(10, 15)]`

Now, B^TA^T = `[(4, 1),(0, 5)] [(1, -1),(2, 3)]`

= `[(4 + 2, -4 + 3),(0 + 10, 0 + 15)]`

= `[(6, -1),(10, 15)]`

= (AB)^T 

Hence proved.