Question

Given A = `[("p", 0),(0, 2)]`, B = `[(0, -"q"),(1, 0)]`, C = `[(2, -2),(2, 2)]` and if BA = C², find p and q.

Answer 1

BA = `[(0, -"q"),(1, 0)] [("p", 0),(0, 2)]`

= `[(0 - 0, 0 - 2"q"),("p" - 0, 0 + 0)]`

= `[(0, -2"q"),("p", 0)]`

C² = `[(2, -2),(2, 2)] [(2, -2),(2, 2)]`

= `[(4 - 4, -4 - 4),(4 + 4, -4 + 4)]`

= `[(0, -8),(8, 0)]`

But BA = C²

`[(0, -2"q"),("p", 0)] = [(0, -8),(8, 0)]`

– 2q = – 8

q = `8/2` = 4

p = 8

∴ The value of p = 8 and q = 4