Suppose that a 4 × 4 matrix A has eigenvalues λ1 = 1, λ2 = − 3, λ3 = 5, and λ4 = − 5. Use the following method to find det (A).

If
p(λ) = det (λI − A) = λn + c1λn − 1 + ⋯ + cn

So, on setting λ = 0, we obtain that

det (− A) = cn or det (A) = (− 1)ncn

det (A) = ?