invOf_eq_nonsing_inv — Mathlib

English

The nonsingular inverse equals invOf when the matrix is invertible.

Русский

Незаключительная обратная равна invOf тогда, когда матрица обращима.

LaTeX

$$$A\\text{Invertible} \\Rightarrow A^{-1} = A^{-1}_{\\mathrm{std}}$$$

Lean4

/-- The nonsingular inverse is the same as `invOf` when `A` is invertible. -/
@[simp]
theorem invOf_eq_nonsing_inv [Invertible A] : ⅟A = A⁻¹ :=
  by
  letI := detInvertibleOfInvertible A
  rw [inv_def, Ring.inverse_invertible, invOf_eq]

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