Question

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

(bA)^T = `[(-2, -4),(2, -6)]^"T"`  .....[∵ b = –2]

= `[(-2, 2),(-4, -6)]`

And A^T = `[(1, -1),(2, 3)]`

∴ bA^T = `[(-2, 2),(-4, -6)]`

= (bA)^T 

Hence proved.