Determinant From Eigenvalues

The determinant of a matrix equals the product of its eigenvalues, counted with multiplicity.

Multiply the three given eigenvalues directly.

1. 1. Apply the determinant-eigenvalue identity

   For any square matrix, the determinant equals the product of its eigenvalues.

   $$\det (A)=2\times 4\times 5$$

2. 2. Multiply

   Multiplying the eigenvalues gives the determinant.

   $$\det (A)=40$$

Answer: 40