adjugate_subsingleton — Mathlib

English

For a matrix A with Finite index set of size 1, adjugate A = 1 (the identity).

Русский

Для матрицы A с одной вершиной индексов adjugate A = 1 (тождество).

LaTeX

$$$\operatorname{adj}(A) = I_n$ \text{ if } \mathrm{card}(n) = 1$$

Lean4

theorem adjugate_subsingleton [Subsingleton n] (A : Matrix n n α) : adjugate A = 1 :=
  by
  ext i j
  simp [Subsingleton.elim i j, adjugate_apply, det_eq_elem_of_subsingleton _ i, one_apply]

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