diff --git a/test/Solve-test.jl b/test/Solve-test.jl
index faec45d3ff..c392edaa9b 100644
--- a/test/Solve-test.jl
+++ b/test/Solve-test.jl
@@ -209,6 +209,13 @@ end
   C = solve_init(M)
   @test_throws ErrorException solve(AbstractAlgebra.Solve.RREFTrait(), C, [R(1), R(2), R(3), R(4), R(5)])
   @test_throws ErrorException solve(AbstractAlgebra.Solve.RREFTrait(), C, matrix(R, 1, 5, [1, 2, 3, 4, 5]))
+
+  # This should work
+  K = kernel(AbstractAlgebra.Solve.RREFTrait(), C)
+  @test nrows(K) == 0
+
+  # This should not
+  @test_throws ErrorException kernel(AbstractAlgebra.Solve.HermiteFormTrait(), C)
 end
 
 @testset "Lazy transpose" begin