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Let A $\in$ Mat$_n (\mathbb{F})$ and let $f(x) = a_n x^n+\cdots+a_1 x+a_0$ be the characteristic polynomial of A. Prove that A is singular if and only if $a_{0} \neq 0$.

Any hint or technique.

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    I presume you mean iff $a_0 = 0$ since otherwise $\det A = (-1)^n a_0 \neq 0$.2012-12-03

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