diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index c9171c3..eef4c06 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -38,8 +38,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.6'
-          - '1'
+          - '1.9'
         os:
           - ubuntu-latest
           - macOS-latest
diff --git a/Project.toml b/Project.toml
index fd3a92d..9a5b673 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.6.24"
+version = "0.7"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -24,10 +24,10 @@ BlockBandedMatrices = "0.12"
 FillArrays = "1"
 InfiniteArrays = "0.13"
 LazyArrays = "1.3"
-LazyBandedMatrices = "0.8.7"
-MatrixFactorizations = "1, 2"
+LazyBandedMatrices = "0.8.7, 0.9"
+MatrixFactorizations = "2.1"
 SemiseparableMatrices = "0.3"
-julia = "1.6"
+julia = "1.9"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
diff --git a/src/InfiniteLinearAlgebra.jl b/src/InfiniteLinearAlgebra.jl
index 3763bf2..ea5d85d 100644
--- a/src/InfiniteLinearAlgebra.jl
+++ b/src/InfiniteLinearAlgebra.jl
@@ -16,14 +16,14 @@ import BandedMatrices: BandedMatrix, _BandedMatrix, AbstractBandedMatrix, banded
                         _default_banded_broadcast, banded_similar
 import FillArrays: AbstractFill, getindex_value, axes_print_matrix_row
 import InfiniteArrays: OneToInf, InfUnitRange, Infinity, PosInfinity, InfiniteCardinal, InfStepRange, AbstractInfUnitRange, InfAxes, InfRanges
-import LinearAlgebra: matprod, qr, AbstractTriangular, AbstractQ, adjoint, transpose, AdjOrTrans
+import LinearAlgebra: matprod, qr, AbstractTriangular, AbstractQ, adjoint, transpose, AdjOrTrans, copymutable
 import LazyArrays: applybroadcaststyle, CachedArray, CachedMatrix, CachedVector, DenseColumnMajor, FillLayout, ApplyMatrix, check_mul_axes, LazyArrayStyle,
                     resizedata!, MemoryLayout, AbstractLazyLayout,
                     factorize, sub_materialize, LazyLayout, LazyArrayStyle, layout_getindex,
                     applylayout, ApplyLayout, PaddedLayout, CachedLayout, AbstractCachedVector, AbstractCachedMatrix, cacheddata, zero!, MulAddStyle, ApplyArray,
                     LazyArray, LazyMatrix, LazyVector, paddeddata, arguments, resizedata!, simplifiable, simplify, LazyLayouts
 import MatrixFactorizations: ul, ul!, _ul, ql, ql!, _ql, QLPackedQ, getL, getR, getQ, getU, reflector!, reflectorApply!, QL, QR, QRPackedQ,
-                            QRPackedQLayout, AdjQRPackedQLayout, QLPackedQLayout, AdjQLPackedQLayout, LayoutQ
+                            QRPackedQLayout, AdjQRPackedQLayout, QLPackedQLayout, AdjQLPackedQLayout, LayoutQ, copymutable_size
 
 import BlockArrays: AbstractBlockVecOrMat, sizes_from_blocks, _length, BlockedUnitRange, blockcolsupport, BlockLayout, AbstractBlockLayout, BlockSlice
 
diff --git a/src/banded/infqltoeplitz.jl b/src/banded/infqltoeplitz.jl
index ccf037f..062baf0 100644
--- a/src/banded/infqltoeplitz.jl
+++ b/src/banded/infqltoeplitz.jl
@@ -83,6 +83,9 @@ function ql_pruneband(A; kwds...)
     Q, H
 end
 
+
+copymutable_size(::NTuple{2,InfiniteCardinal{0}}, Q) = cache(Q)
+
 # represent Q as a product of orthogonal operations
 struct ProductQ{T,QQ<:Tuple} <: LayoutQ{T}
     Qs::QQ
@@ -141,7 +144,6 @@ mul(Q::ProductQ, X::AbstractMatrix) = ApplyArray(*, Q.Qs...) * X
 mul(X::AbstractMatrix, Q::ProductQ) = X * ApplyArray(*, Q.Qs...)
 
 
-
 # LQ where Q is a product of orthogonal operations
 struct QLProduct{T,QQ<:Tuple,LL} <: Factorization{T}
     Qs::QQ
diff --git a/test/test_infql.jl b/test/test_infql.jl
index fe0e22c..a3dc5b0 100644
--- a/test/test_infql.jl
+++ b/test/test_infql.jl
@@ -197,6 +197,8 @@ using ArrayLayouts: TriangularLayout, UnknownLayout
             @test (Q*L)[1:10,1:10] ≈ A[1:10,1:10]
 
             @test (L*Q)[1:10,1:10] ≈ LazyBandedMatrices.SymTridiagonal(L*Q)[1:10,1:10]
+            @test Q[5,6:8] == [Q[5,k] for k = 6:8]
+            @test Q[6:8,5] == [Q[k,5] for k = 6:8]
         end
 
         @test_throws ErrorException ql(zeros(∞,∞))