`BookProof.ChapterA3.adj2_mul_T` (T : Matrix (Fin 2) (Fin 2) ℂ) (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) : adj2 T * T = 1

Proved

BookProof.ChapterA3.adj2_mul_T

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3i.

BookProof.ChapterA3.adj2_mul_T (T : Matrix (Fin 2) (Fin 2) ℂ) (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) : adj2 T * T = 1

Formalization note: Lean 4 identifier BookProof.ChapterA3.adj2_mul_T.

Preamble

-- Generated from ChapterA3i.lean — theorem BookProof.ChapterA3.adj2_mul_T
import Mathlib
import Definitions.Def_ChapterA3i
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.adj2_mul_T (T : Matrix (Fin 2) (Fin 2) ℂ)
    (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) :
    adj2 T * T = 1 := by sorry

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