Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A

Suppose that the characteristic polynomial of A is

p_A (x) = a₀ + a₁x + a₂x² + · · · + a_nxⁿ

Then

a₀ = a₀ + a₁(0) + a₂(0)² + · · · + a_n(0)ⁿ

= p_A (0)

= det (A − 0I_n)                                                                                 Definition CP

= det (A)