If `A=[(1 ,0, 2), (0, 2, 1), (2, 0, 3)]` , then show that `A` is a root of the polynomial `f(x)=x^3-6x^2+7x+2` .

Explanation

Given that,

`A= [(1 ,0, 2), (0, 2, 1), (2, 0, 3)]`

so,`A^2= [(1 ,0, 2), (0, 2, 1), (2, 0, 3)]xx [(1 ,0, 2), (0, 2, 1), (2, 0, 3)]`

`=[(5,0,8),(2,4,5),(8,0,13)]`

And `A^3=A^2xxA=[(5,0,8),(2,4,5),(8,0,13)]xx [(1 ,0, 2), (0, 2, 1), (2, 0, 3)]`

`implies A^3=[(21,0,34),(12,8,23),(34,0,55)]`

`f(x)=x^3-6x^2+7x+2`

We have to show that, `f(A)=A^3-6A^2+7A+2I=0`

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