diff --git a/Project.toml b/Project.toml
index 5c84a8b2..32c6f9be 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ArrayInterface"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "7.4.11"
+version = "7.5.0"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/ext/ArrayInterfaceBandedMatricesExt.jl b/ext/ArrayInterfaceBandedMatricesExt.jl
index 358434f1..a3b8ca67 100644
--- a/ext/ArrayInterfaceBandedMatricesExt.jl
+++ b/ext/ArrayInterfaceBandedMatricesExt.jl
@@ -1,16 +1,26 @@
 module ArrayInterfaceBandedMatricesExt
 
-
 if isdefined(Base, :get_extension)
     using ArrayInterface
     using ArrayInterface: BandedMatrixIndex
     using BandedMatrices
+    using LinearAlgebra
 else
     using ..ArrayInterface
     using ..ArrayInterface: BandedMatrixIndex
     using ..BandedMatrices
+    using ..LinearAlgebra
 end
 
+const TransOrAdjBandedMatrix = Union{
+    Adjoint{T, <:BandedMatrix{T}},
+    Transpose{T, <:BandedMatrix{T}},
+} where {T}
+
+const AllBandedMatrix = Union{
+    BandedMatrix{T},
+    TransOrAdjBandedMatrix{T},
+} where {T}
 
 Base.firstindex(i::BandedMatrixIndex) = 1
 Base.lastindex(i::BandedMatrixIndex) = i.count
@@ -45,12 +55,12 @@ end
 
 function BandedMatrixIndex(rowsize, colsize, lowerbandwidth, upperbandwidth, isrow)
     upperbandwidth > -lowerbandwidth || throw(ErrorException("Invalid Bandwidths"))
-    bandinds = upperbandwidth:-1:-lowerbandwidth
+    bandinds = upperbandwidth:-1:(-lowerbandwidth)
     bandsizes = [_bandsize(band, rowsize, colsize) for band in bandinds]
     BandedMatrixIndex(sum(bandsizes), rowsize, colsize, bandinds, bandsizes, isrow)
 end
 
-function ArrayInterface.findstructralnz(x::BandedMatrices.BandedMatrix)
+function ArrayInterface.findstructralnz(x::AllBandedMatrix)
     l, u = BandedMatrices.bandwidths(x)
     rowsize, colsize = Base.size(x)
     rowind = BandedMatrixIndex(rowsize, colsize, l, u, true)
@@ -58,11 +68,11 @@ function ArrayInterface.findstructralnz(x::BandedMatrices.BandedMatrix)
     return (rowind, colind)
 end
 
-ArrayInterface.has_sparsestruct(::Type{<:BandedMatrices.BandedMatrix}) = true
-ArrayInterface.isstructured(::Type{<:BandedMatrices.BandedMatrix}) = true
-ArrayInterface.fast_matrix_colors(::Type{<:BandedMatrices.BandedMatrix}) = true
+ArrayInterface.has_sparsestruct(::Type{<:AllBandedMatrix}) = true
+ArrayInterface.isstructured(::Type{<:AllBandedMatrix}) = true
+ArrayInterface.fast_matrix_colors(::Type{<:AllBandedMatrix}) = true
 
-function ArrayInterface.matrix_colors(A::BandedMatrices.BandedMatrix)
+function ArrayInterface.matrix_colors(A::AllBandedMatrix)
     l, u = BandedMatrices.bandwidths(A)
     width = u + l + 1
     return ArrayInterface._cycle(1:width, Base.size(A, 2))
diff --git a/test/bandedmatrices.jl b/test/bandedmatrices.jl
index a6142efd..94626aac 100644
--- a/test/bandedmatrices.jl
+++ b/test/bandedmatrices.jl
@@ -1,19 +1,50 @@
-
 using ArrayInterface
 using BandedMatrices
 using Test
 
-B=BandedMatrix(Ones(5,5), (-1,2))
-B[band(1)].=[1,2,3,4]
-B[band(2)].=[5,6,7]
+function checkequal(idx1::ArrayInterface.BandedMatrixIndex,
+    idx2::ArrayInterface.BandedMatrixIndex)
+    return idx1.rowsize == idx2.rowsize && idx1.colsize == idx2.colsize &&
+           idx1.bandinds == idx2.bandinds && idx1.bandsizes == idx2.bandsizes &&
+           idx1.isrow == idx2.isrow && idx1.count == idx2.count
+end
+
+B = BandedMatrix(Ones(5, 5), (-1, 2))
+B[band(1)] .= [1, 2, 3, 4]
+B[band(2)] .= [5, 6, 7]
 @test ArrayInterface.has_sparsestruct(B)
-rowind,colind=ArrayInterface.findstructralnz(B)
-@test [B[rowind[i],colind[i]] for i in 1:length(rowind)]==[5,6,7,1,2,3,4]
-B=BandedMatrix(Ones(4,6), (-1,2))
-B[band(1)].=[1,2,3,4]
-B[band(2)].=[5,6,7,8]
-rowind,colind=ArrayInterface.findstructralnz(B)
-@test [B[rowind[i],colind[i]] for i in 1:length(rowind)]==[5,6,7,8,1,2,3,4]
+rowind, colind = ArrayInterface.findstructralnz(B)
+@test [B[rowind[i], colind[i]] for i in 1:length(rowind)] == [5, 6, 7, 1, 2, 3, 4]
+B = BandedMatrix(Ones(4, 6), (-1, 2))
+B[band(1)] .= [1, 2, 3, 4]
+B[band(2)] .= [5, 6, 7, 8]
+rowind, colind = ArrayInterface.findstructralnz(B)
+@test [B[rowind[i], colind[i]] for i in 1:length(rowind)] == [5, 6, 7, 8, 1, 2, 3, 4]
 @test ArrayInterface.isstructured(typeof(B))
 @test ArrayInterface.fast_matrix_colors(typeof(B))
 
+for op in (adjoint, transpose)
+    B = BandedMatrix(Ones(5, 5), (-1, 2))
+    B[band(1)] .= [1, 2, 3, 4]
+    B[band(2)] .= [5, 6, 7]
+    B′ = op(B)
+    @test ArrayInterface.has_sparsestruct(B′)
+    rowind′, colind′ = ArrayInterface.findstructralnz(B′)
+    rowind′′, colind′′ = ArrayInterface.findstructralnz(BandedMatrix(B′))
+    @test checkequal(rowind′, rowind′′)
+    @test checkequal(colind′, colind′′)
+
+    B = BandedMatrix(Ones(4, 6), (-1, 2))
+    B[band(1)] .= [1, 2, 3, 4]
+    B[band(2)] .= [5, 6, 7, 8]
+    B′ = op(B)
+    rowind′, colind′ = ArrayInterface.findstructralnz(B′)
+    rowind′′, colind′′ = ArrayInterface.findstructralnz(BandedMatrix(B′))
+    @test checkequal(rowind′, rowind′′)
+    @test checkequal(colind′, colind′′)
+
+    @test ArrayInterface.isstructured(typeof(B′))
+    @test ArrayInterface.fast_matrix_colors(typeof(B′))
+
+    @test ArrayInterface.matrix_colors(B′) == ArrayInterface.matrix_colors(BandedMatrix(B′))
+end