case left
n : Type u
inst✝³ : DecidableEq n
inst✝² : Fintype n
α : Type v
inst✝¹ : CommRing α
inst✝ : StarRing α
A✝ A : Matrix n n α
hA : A ∈ unitaryGroup n α
⊢ star (det A) * det A = 1

case right
n : Type u
inst✝³ : DecidableEq n
inst✝² : Fintype n
α : Type v
inst✝¹ : CommRing α
inst✝ : StarRing α
A✝ A : Matrix n n α
hA : A ∈ unitaryGroup n α
⊢ det A * star (det A) = 1
n : Type u
inst✝³ : DecidableEq n
inst✝² : Fintype n
α : Type v
inst✝¹ : CommRing α
inst✝ : StarRing α
A✝ A : Matrix n n α
hA : A ∈ unitaryGroup n α
⊢ det A ∈ unitary α
constructor
no goals
case left
n : Type u
inst✝³ : DecidableEq n
inst✝² : Fintype n
α : Type v
inst✝¹ : CommRing α
inst✝ : StarRing α
A✝ A : Matrix n n α
hA : A ∈ unitaryGroup n α
⊢ star (det A) * det A = 1
simpa [star, det_transpose] using congr_arg det hA.1
no goals
case right
n : Type u
inst✝³ : DecidableEq n
inst✝² : Fintype n
α : Type v
inst✝¹ : CommRing α
inst✝ : StarRing α
A✝ A : Matrix n n α
hA : A ∈ unitaryGroup n α
⊢ det A * star (det A) = 1
simpa [star, det_transpose] using congr_arg det hA.2