What is the characteristic polynomial χA(x) and how do I prove it for a 2×2 matrix?

[Chewybakas]

Homework Statement

Let A ε M2x2 prove χA(x) = x^2 -tr(A)x + det(A)

Homework Equations

The Attempt at a Solution

Hi all, this is an assignment equation and the right hand side i can perfectly understand but i can't understand the left hand side, What is it i am looking for?? Can anyone help?

 

[Dick]

Homework Statement

Let A ε M2x2 prove χA(x) = x^2 -tr(A)x + det(A)

Homework Equations

The Attempt at a Solution

Hi all, this is an assignment equation and the right hand side i can perfectly understand but i can't understand the left hand side, What is it i am looking for?? Can anyone help?

The left side looks like it is supposed to be the characteristic polynomial of A.