Question

If A = `[(4,5),(2,1)]` and A² - 5A - 6l = 0, then A^-1 = ?

Options

• `1/6 [(-1,5),(-2,-4)]`

• `1/6 [(-1,5),(2,4)]`

• `1/6 [(-1,5),(2,-4)]`

• `1/6[(1,5),(2,-4)]`

Answer 1

`1/6 [(-1,5),(2,-4)]`

Explanation:

We have,

A = `[(4,5),(2,1)]`

and A² - 5A - 6l = 0

6l = A² - 5A

Multiply by A^-1, we get

6A^-1 = A - 5I

`6"A"^-1 = [(4,5),(2,1)] - [(5,0),(0,5)]`

`6"A"^-1 = [(-1,5),(2,-4)]`

`"A"^-1 = 1/6 [(-1,5),(2,-4)]`