Question

If A = `[(a, 0),(0, 2)]`, B = `[(0, -b),(1, 0)]`, M = `[(1, -1),(1, 1)]` and BA = M², find the values of a and b.

Answer 1

BA = `[(0, -b),(1, 0)][(a, 0),(0, 2)]`

= `[(0 xx a + (-b) xx 0, 0 xx 0 + (-b) xx 2),(1 xx a + 0 xx 0, 1 xx 0 + 0 xx 2)]`

= `[(0 - 0,0 - 2b),(a + 0, 0 + 0)]`

= `[(0, -2b), (a, 0)]`

M² = `[(1 ,-1),(1, 1)][(1, -1),(1, 1)]`

= `[(1 xx 1 + (-1) xx 1, 1 xx (-1) + (-1 xx 1)),(1 xx 1 + 1 xx 1, 1 xx (-1) + 1 xx 1)]`

= `[(1 - 1, -1 - 1),(1 + 1, -1 + 1)]`

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

Given, BA = M²

`[(0, -2b),(a, 0)] = [(0, -2),(2, 0)]`

Comparing the corresponding elements, we get,

a = 2

–2b = –2 `=>` b = 1