Question

If A = `[(3, 1),(-1, 2)]` show that A² – 5A + 7I = 0.

Answer 1

We have to proved that A² – 5A + 7I = 0

`A^2 = [(3, 1), (-1, 2)][(3, 1), (-1, 2)]`

= `[(9 - 1, 3 + 2),(-3 - 2, -1 + 4)]`

= `[(8, 5), (-5, 3)]`

`5A = 5[(3, 1), (-1, 2)] = [(15, 5), (-5, 10)]`

Now, substituting the values in A² – 5A + 71, we have,

`A^2 - 5A + 7I = [(8, 5), (-5, 3)] - [(15, 5),(-5, 10)] + [(7, 0),(0, 7)]`

= `[(-7, 0), (0, -7)] + [(7, 0), (0, 7)]`

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

= 0