Question

If A = `[(1, "a"),(0, 1)]`, then compute A⁴ 

Answer 1

A = `[(1, "a"),(0, 1)]`

A² = A . A

= `[(1, "a"),(0, 1)] [(1, "a"),(0, 1)]`

= `[(1 + 0, "a" + "a"),(0 + 0, 0 + 1)]`

A² = `[(1, 2"a"),(0, 1)]`

A⁴ = A² × A² 

= `[(1, "a"),(0, 1)] [(1, 2"a"),(0, 1)]`

A⁴ = `[(1 + 0, 2"a" + 2"a"),(0 + 0, 0 +  1)]`

A⁴ = `[(1, 4"a"),(0, 1)]`