Add inv(::AbstractQ) (#35826)

* Override `inv` for `AbstractQ`

* Add test for inv

* Update qr.jl

Co-authored-by: Andreas Noack <andreas@noack.dk>

Author: dlfivefifty

stdlib/LinearAlgebra/src/qr.jl

@@ -467,6 +467,8 @@ Base.propertynames(F::QRPivoted, private::Bool=false) =
 
 abstract type AbstractQ{T} <: AbstractMatrix{T} end
 
+inv(Q::AbstractQ) = Q'
+
 """
     QRPackedQ <: AbstractMatrix
 

stdlib/LinearAlgebra/test/qr.jl

@@ -297,4 +297,11 @@ end
     end
 end
 
+@testset "inv(::AbstractQ)" begin
+    for T in (Float64, ComplexF64)
+        Q = qr(randn(T,5,5)).Q
+        @test inv(Q) === Q'
+    end
+end
+
 end # module TestQR