Answer: A2 = A.
- A A2 = I
- B A2 = 0
- C A2 = A
- D A = AT
Correct answer: C. A2 = A
Explanation: A is idempotent when A² = A. Consequence: eigenvalues satisfy λ² = λ, so λ = 0 or 1. Example: projection matrices P = A(AᵀA)⁻¹Aᵀ are idempotent. Applying the transformation twice has the same effect as once. Answer: A² = A.
Concept context
Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.