diff --git a/test/runtests.jl b/test/runtests.jl
index 40b921b..43d6217 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -76,6 +76,12 @@ end
         @test D' * M ≈ D' * Mf
         @test M * E' ≈ Mf * E'
         @test E * M' ≈ E * Mf'
+        @test size(Mf, 1) == 15
+        @test size(Mf, 2) == 10
+        @test size(Mf, 3) == 1
+        @test length(Mf) == 150
+        @test similar(Mf, (3, 4)) isa Matrix{eltype(U)}
+        @test similar(Mf, Int, (3, 4)) isa Matrix{Int}
         @test !any(isnan, Mf)
         @test !any(isinf, Mf)
         V1, U1 = [1; 1;;], [1 -1]
@@ -203,6 +209,21 @@ end
             check_fmfm_fm_alloc(Mf, Mf_A, ws3x3, Cf15x8)
         end
 
+        # mul! FM×FM→FM: elseif branch (k-rank output) and DimensionMismatch
+        let
+            Ua = myrand(T, 15, 2); Va = myrand(T, 2, 10)
+            Ub = myrand(T, 10, 3); Vb = myrand(T, 3, 8)
+            Af = FactoredMatrix(Ua, Va); Bf = FactoredMatrix(Ub, Vb)
+            expected = (Ua * Va) * (Ub * Vb)
+            # k-rank output (C rank = k = 2)
+            Ck = FactoredMatrix(Matrix{T}(undef, 15, 2), Matrix{T}(undef, 2, 8))
+            mul!(Ck, Af, Bf)
+            @test Array(Ck) ≈ expected
+            # wrong rank → DimensionMismatch
+            Cbad = FactoredMatrix(Matrix{T}(undef, 15, 4), Matrix{T}(undef, 4, 8))
+            @test_throws DimensionMismatch("C's factorization size doesn't match the result of A*B") mul!(Cbad, Af, Bf)
+        end
+
         # mul! vector (with and without cache)
         let
             b = vec(myrand(T, 10, 1))