diff --git a/tests/cpp/test_matmul_scheduler.cpp b/tests/cpp/test_matmul_scheduler.cpp
index ef68909601e..a3b72013be6 100644
--- a/tests/cpp/test_matmul_scheduler.cpp
+++ b/tests/cpp/test_matmul_scheduler.cpp
@@ -3075,6 +3075,80 @@ TEST_F(MatmulSchedulerTest, OperandOrderIssue2434) {
   NVF_CHECK(cg_outputs[0].allclose(tref, 0.0001, 0.0001));
 }
 
+TEST_F(MatmulSchedulerTest, HSH_TT) {
+  NVFUSER_TEST_CUDA_ARCH_RANGE_GUARD(8, 0, 10, 0);
+  auto fusion = std::make_unique<Fusion>();
+  FusionGuard fg(fusion.get());
+
+  const auto dtype = DataType::Half;
+  constexpr auto layout = MmaLayout::TT;
+
+  auto tv0 = makeContigConcreteTensor({-1, -1, 1}, dtype); // A [M, K, b]
+  auto tv1 = makeContigConcreteTensor({1, -1, -1}, dtype); // B [b, K, N]
+  fusion->addInput(tv0);
+  fusion->addInput(tv1);
+
+  auto tv2 = fusedMultiplySum(tv0, tv1, {1});
+
+  // Reorder the accumulator as [M, N, K]
+  // [M, rK, N] -> [M, N, K]
+  tv2->reorder({{-2, -1}, {-1, -2}});
+  tv2->commitLeafToLogical();
+
+  auto tv3 = castOp(DataType::Half, tv2);
+  fusion->addOutput(tv3);
+
+  NVF_CHECK(
+      1 == ir_utils::getOpsOfType<MmaOp>(fusion.get()).size(),
+      "matmul fusion must have at least one MmaOp");
+
+  // Create custom Matmul Params
+  MatMulTileOptions gemm_tile;
+  // TODO cta tile is a multiple of mma macro for hopper.
+  gemm_tile.cta_tile = GemmTile(128, 128, 32);
+
+  // TODO warp tile is (macroM, macroN, macroK) for hopper.
+  gemm_tile.warp_tile = GemmTile(64, 64, 32);
+
+  // TODO instruction tile is not used for hopper.
+  gemm_tile.instruction_tile = GemmTile(16, 8, 16);
+
+  MatmulParams mparams;
+  mparams.supported_vec_size = {8, 8, 4};
+
+  // TODO use hopper macro
+  // mparams.mma_macro = MmaMacro::Hopper_64_256_16;
+  mparams.mma_macro = MmaMacro::Ampere_16_8_16;
+
+  mparams.tile_sizes = gemm_tile;
+  mparams.async_gmem_load_operands = true;
+  mparams.circular_buffer_options.circular_buffer_smem_write = true;
+  mparams.circular_buffer_options.circular_buffer_smem_read = true;
+  mparams.circular_buffer_options.smem_circular_buffer_stage = 4;
+
+  // TODO Create prefetch parameter
+  // mparams.circular_buffer_options.smem_circular_buffer_prefetch = 3;
+
+  // Schedule matmul fusion using custom parameters
+  SchedulerEntry::makeSchedulerInstance(SchedulerType::Matmul)
+      ->schedule(fusion.get(), &mparams);
+
+  const int M = 32, N = 32, K = 256;
+  auto inputs =
+      matmulAtInput3DHopperSS(M, N, K, layout, data_type_to_aten(dtype));
+
+  FusionExecutor fe;
+  fe.compileFusion(
+      fusion.get(),
+      {inputs.first, inputs.second},
+      LaunchParams(),
+      matmul_cparams);
+
+  auto cg_outputs = fe.runFusion({inputs.first, inputs.second});
+  auto tref = atMatmul(inputs.first.squeeze(), inputs.second.squeeze(), layout);
+  EXPECT_TRUE(at::allclose(cg_outputs[0], tref, 1e-5, 1e-5));
+}
+
 TEST_F(MatmulSchedulerTest, HSH_TN) {
   NVFUSER_TEST_CUDA_ARCH_RANGE_GUARD(8, 0, 10, 0);
   auto fusion = std::make_unique<Fusion>();
@@ -3221,4 +3295,78 @@ TEST_F(MatmulSchedulerTest, HSH_NT) {
   EXPECT_TRUE(at::allclose(cg_outputs[0], tref, 1e-5, 1e-5));
 }
 
+TEST_F(MatmulSchedulerTest, HSH_NN) {
+  NVFUSER_TEST_CUDA_ARCH_RANGE_GUARD(8, 0, 10, 0);
+  auto fusion = std::make_unique<Fusion>();
+  FusionGuard fg(fusion.get());
+
+  const auto dtype = DataType::Half;
+  constexpr auto layout = MmaLayout::NN;
+
+  auto tv0 = makeContigConcreteTensor({1, -1, -1}, dtype); // A [b, K, M]
+  auto tv1 = makeContigConcreteTensor({-1, -1, 1}, dtype); // B [N, K, 1]
+  fusion->addInput(tv0);
+  fusion->addInput(tv1);
+
+  auto tv2 = fusedMultiplySum(tv0, tv1, {1});
+
+  // Reorder the accumulator as [M, N, K]
+  // [N, rK, M] -> [M, N, K]
+  tv2->reorder({{-1, -3}});
+  tv2->commitLeafToLogical();
+
+  auto tv3 = castOp(DataType::Half, tv2);
+  fusion->addOutput(tv3);
+
+  NVF_CHECK(
+      1 == ir_utils::getOpsOfType<MmaOp>(fusion.get()).size(),
+      "matmul fusion must have at least one MmaOp");
+
+  // Create custom Matmul Params
+  MatMulTileOptions gemm_tile;
+  // TODO cta tile is a multiple of mma macro for hopper.
+  gemm_tile.cta_tile = GemmTile(128, 128, 32);
+
+  // TODO warp tile is (macroM, macroN, macroK) for hopper.
+  gemm_tile.warp_tile = GemmTile(64, 64, 32);
+
+  // TODO instruction tile is not used for hopper.
+  gemm_tile.instruction_tile = GemmTile(16, 8, 16);
+
+  MatmulParams mparams;
+  mparams.supported_vec_size = {8, 8, 4};
+
+  // TODO use hopper macro
+  // mparams.mma_macro = MmaMacro::Hopper_64_256_16;
+  mparams.mma_macro = MmaMacro::Ampere_16_8_16;
+
+  mparams.tile_sizes = gemm_tile;
+  mparams.async_gmem_load_operands = true;
+  mparams.circular_buffer_options.circular_buffer_smem_write = true;
+  mparams.circular_buffer_options.circular_buffer_smem_read = true;
+  mparams.circular_buffer_options.smem_circular_buffer_stage = 4;
+
+  // TODO Create prefetch parameter
+  // mparams.circular_buffer_options.smem_circular_buffer_prefetch = 3;
+
+  // Schedule matmul fusion using custom parameters
+  SchedulerEntry::makeSchedulerInstance(SchedulerType::Matmul)
+      ->schedule(fusion.get(), &mparams);
+
+  const int M = 32, N = 32, K = 256;
+  auto inputs =
+      matmulAtInput3DHopperSS(M, N, K, layout, data_type_to_aten(dtype));
+
+  FusionExecutor fe;
+  fe.compileFusion(
+      fusion.get(),
+      {inputs.first, inputs.second},
+      LaunchParams(),
+      matmul_cparams);
+
+  auto cg_outputs = fe.runFusion({inputs.first, inputs.second});
+  auto tref = atMatmul(inputs.first.squeeze(), inputs.second.squeeze(), layout);
+  EXPECT_TRUE(at::allclose(cg_outputs[0], tref, 1e-5, 1e-5));
+}
+
 } // namespace nvfuser