Question

If M = `[(1, 2),(2, 1)]` and I is a unit matrix of the same order as that of M; show that: M² = 2M + 3I.

Answer 1

M² = `[(1, 2),(2, 1)][(1, 2),(2, 1)]`

= `[(1 xx 1 + 2 xx 2, 1 xx 2 + 2 xx 1),(2 xx 1 + 1 xx 2, 2 xx 2 + 1 xx 1)]`

= `[(1 + 4, 2 + 2),(2 + 2, 4 + 1)]`

= `[(5, 4),(4, 5)]`

2M + 3I = `2[(1, 2),(2, 1)] + 3[(1, 0),(0, 1)]`

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

= `[(5, 4),(4, 5)]`

Hence, M² = 2M + 3I