Answer: det(A) = 0.
- A det(A) is not zero
- B A is invertible
- C det(A) = 0
- D A has distinct eigenvalues
Correct answer: C. det(A) = 0
Explanation: AX = 0 has a non-trivial (non-zero) solution only when det(A) = 0, i.e., the matrix is singular.
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.