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Math Help - Characteristic Polynomial

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    Characteristic Polynomial

    Let A be 2x2 and let p(\lambda)=\lambda^2+b\lambda+c be the characteristic polynomial of A. Show that b=-tr(A) and c=det(A).

    I know with a 2x2 matrix that \lambda^2-tr(A)\lambda+det(A) forms the characteristic polynomial; however, I am not sure on how to prove it. I am guessing it is probably trivial if I know that.
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    I know what the website is saying. The problem is in making it coherent and mathematical correct in the proof.
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    Let A = \left(\begin{array}{cc}a&b\\c&d\end{array}\right)

    Then find the charateristic polynomial

    p(\lambda) = \left|\begin{array}{cc}a-\lambda &b\\c&d-\lambda1\end{array}\right|

    Then find the trace and the deteminant. The rest is up to you
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