Question

Answer the following question:

If A = `[(2, 1),(0, 3)]`, B = `[(1, 2),(3, -2)]`, verify that |AB| = |A||B|

Answer 1

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

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

= `[(5, 2),(9, -6)]`

∴ |AB| = `|(5, 2),(9, -6)|` 

= –30 – 18

= – 48  ...(1)

|A| = `|(2, 1),(0, 3)|` = 6 – 0 = 6

|B| = `|(1, 2),(3, -2)|` = –2 – 6 = – 8

∴ |A||B| = 6 ( – 8)

= – 48  ...(2)

From (1) and (2),

|AB| = |A||B|