lean_workbook_plus_51508

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $A,B \in M(n,C)$ be matrices such that $AB=A$ and $BA=B$ . Prove that $(A-B)^2=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51508 {n : ℕ} (A B : Matrix (Fin n) (Fin n) ℂ) (hAB : A * B = A) (hBA : B * A = B) : (A - B) ^ 2 = 0   :=  by sorry

Source