Question

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

Answer 1

We have,

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

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

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

And a = 4, b = –2

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

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

∴ (A^T)^T = `[(1, -1),(2, 3)]^"T"`

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

= A

Hence proved.