Proving χA(x) = x^2 -tr(A)x + det(A) for Matrix A in Linear Algebra Homework

Chewybakas
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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?
 
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Chewybakas said:

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.
 

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