Answer: det(A).
- A det(A)
- B trace(A)
- C n (the order)
- D Sum of eigenvalues
Correct answer: A. det(A)
Explanation: The characteristic polynomial det(λI−A) = λⁿ − (tr A)λⁿ⁻¹ + … + (−1)ⁿdet(A). The constant term (product of all roots with sign) equals det(A). So product of eigenvalues = det(A). Answer: det(A).
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.