• Oct 3, 2025 Idempotent Matrix A, then multiplying both sides by A⁻¹ gives A = I. Transpose: The transpose of an idempotent matrix (Aᵀ) is also idempotent. This follows from (Aᵀ)² = (A²)ᵀ = Aᵀ. Nilpotency: While not directly relate BY Sally Kovacek