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.
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.