Let A belonging $\displaystyle M_n$ be a non-singular matrix. Let $\displaystyle p_A(t)$ be its characteristic polynomial, $\displaystyle p_A(t)$ = det(tI-A) = $\displaystyle t^n + a_(n-1)t^(n-1) + ... + a_1t + a_0$.

a) Prove that $\displaystyle a_0 = (-1)^n det(A)$