Question

If A is a solution of x² - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A^-1 equals ______.

Options

• `[[2/3,1/3],[1/3,2/3]]`

• `[[2,-1],[-1,2]]`

• `[[2/3,-1/3],[1/3,-2/3]]`

• `[[3,-1],[1,2]]`

Answer 1

If A is a solution of x² - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A^-1 equals `underline([[2/3,1/3],[1/3,2/3]])`.

Explanation:

A² - 4A+3I= 0

⇒ A- 4I + 3A^-1 = 0

`=>A^-1=1/3(4I-A)`

`therefore A^-1=1/3{[[4,0],[0,4]]-[[2,-1],[-1,2]]}=[[2/3,1/3],[1/3,2/3]]`