Determinant of 3x3 Matrix without direct evaluation

[ZedCar]

Homework Statement

Show that:

(x^2) (2x) (-2)
(2x) (2-x^2) (2x)
(2) (-2x) (-x^2)

= (x^2 + 2)^3

Do not use direct evaluation.

Homework Equations

The Attempt at a Solution

As direct evaluation is not permitted, I'm wondering which method should I use? Thank you

 

[xaos]

what possible methods do you have in mind?

 

[ZedCar]

Is it a method using cofactors?

 

[xaos]

okay, now what does the method of cofactors do?

 

[ZedCar]

I'm going to have to look into that.

I have a sheet which I just got today from lecture and it states;

Cofactor is the minor multiplied by the sign of the element
Cij = (-1)^(i+j) Mij

 

[ZedCar]

Is this cofactor method different from making an upper triangular matrix from it?