Question: Let A be any n ( n real matrix. (a) Prove that the coefficient of (n-1 in the characteristic polynomial of A is given by

Let A be any n ( n real matrix.
(a) Prove that the coefficient of (n-1 in the characteristic polynomial of A is given by - Tr(A).
(b) Prove that Tr(A) is the sum of the eigenvalues of A.
(c) Prove that the constant coefficient of the characteristic polynomial of A is ± times the product of the eigenvalues of A?

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