Question

If A = `[(p, 0),(0, 2)], B = [(0, -q),(1, 0)], C = [(2, -2),(2, 2)]` and BA = C², find the values of p and q.

Answer 1

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

= `[(2 xx 2 + (-2) xx 2, 2 xx (-2) + (-2) xx 2),(2 xx 2 + 2 xx 2, 2 xx (-2) + 2 xx 2)]`

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

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

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

= `[(0 xx p + (-q) xx 0, 0 xx 0 + (-q) xx 2),(1 xx p + 0 xx 0, 1 xx 0 + 0 xx 2)]`

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

Equate BA = C²

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

2q = −8

q = 4

p = 8