A three by three circulant determinant

Proved

WorkbookRestored.plus_50816

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For real $a,b,c$ , $\det\begin{pmatrix}a&b&c\\c&a&b\\b&c&a\end{pmatrix}=a^3+b^3+c^3-3abc$ .

Source: Lean-Workbook row lean_workbook_plus_50816 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic

Formal statement

theorem WorkbookRestored.plus_50816 (a b c : ℝ) :
  Matrix.det (![![a, b, c],![c, a, b],![b, c, a]]) = a^3 + b^3 + c^3 - 3*a*b*c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_50816; immutable original Prove2Me node 51c4ccc2-929a-40e8-bae8-617d1a685430

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