diff --git a/source/opt/aggressive_dead_code_elim_pass.cpp b/source/opt/aggressive_dead_code_elim_pass.cpp
index e9c831e544..44432399ca 100644
--- a/source/opt/aggressive_dead_code_elim_pass.cpp
+++ b/source/opt/aggressive_dead_code_elim_pass.cpp
@@ -1005,6 +1005,7 @@ void AggressiveDCEPass::InitExtensions() {
       "SPV_EXT_shader_atomic_float_add",
       "SPV_EXT_fragment_shader_interlock",
       "SPV_NV_compute_shader_derivatives",
+      "SPV_NV_cooperative_matrix",
       "SPV_KHR_cooperative_matrix"
   });
   // clang-format on
diff --git a/source/opt/folding_rules.cpp b/source/opt/folding_rules.cpp
index 41f535d85d..2ebc385cb4 100644
--- a/source/opt/folding_rules.cpp
+++ b/source/opt/folding_rules.cpp
@@ -112,6 +112,12 @@ bool IsValidResult(T val) {
   }
 }
 
+// Returns true if `type` is a cooperative matrix.
+bool IsCooperativeMatrix(const analysis::Type* type) {
+  return type->kind() == analysis::Type::kCooperativeMatrixKHR ||
+         type->kind() == analysis::Type::kCooperativeMatrixNV;
+}
+
 const analysis::Constant* ConstInput(
     const std::vector<const analysis::Constant*>& constants) {
   return constants[0] ? constants[0] : constants[1];
@@ -314,7 +320,7 @@ FoldingRule ReciprocalFDiv() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -400,7 +406,7 @@ FoldingRule MergeNegateMulDivArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -466,7 +472,7 @@ FoldingRule MergeNegateAddSubArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -702,7 +708,7 @@ FoldingRule MergeMulMulArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -761,7 +767,7 @@ FoldingRule MergeMulDivArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -839,7 +845,7 @@ FoldingRule MergeMulNegateArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -884,7 +890,7 @@ FoldingRule MergeDivDivArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -962,7 +968,7 @@ FoldingRule MergeDivMulArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1109,7 +1115,7 @@ FoldingRule MergeSubNegateArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1162,7 +1168,7 @@ FoldingRule MergeAddAddArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::Kind::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1215,7 +1221,7 @@ FoldingRule MergeAddSubArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::Kind::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1280,7 +1286,7 @@ FoldingRule MergeSubAddArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1351,7 +1357,7 @@ FoldingRule MergeSubSubArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
@@ -1449,7 +1455,7 @@ FoldingRule MergeGenericAddSubArithmetic() {
     const analysis::Type* type =
         context->get_type_mgr()->GetType(inst->type_id());
 
-    if (type->kind() == analysis::Type::kCooperativeMatrixKHR) {
+    if (IsCooperativeMatrix(type)) {
       return false;
     }
 
diff --git a/source/opt/local_access_chain_convert_pass.cpp b/source/opt/local_access_chain_convert_pass.cpp
index 987e9a6b70..174e7d86da 100644
--- a/source/opt/local_access_chain_convert_pass.cpp
+++ b/source/opt/local_access_chain_convert_pass.cpp
@@ -429,7 +429,7 @@ void LocalAccessChainConvertPass::InitExtensions() {
        "SPV_KHR_fragment_shader_barycentric", "SPV_KHR_vulkan_memory_model",
        "SPV_NV_bindless_texture", "SPV_EXT_shader_atomic_float_add",
        "SPV_EXT_fragment_shader_interlock", "SPV_NV_compute_shader_derivatives",
-       "SPV_KHR_cooperative_matrix"});
+       "SPV_NV_cooperative_matrix", "SPV_KHR_cooperative_matrix"});
 }
 
 bool LocalAccessChainConvertPass::AnyIndexIsOutOfBounds(
diff --git a/source/opt/local_single_block_elim_pass.cpp b/source/opt/local_single_block_elim_pass.cpp
index dd0b594a9d..3a7d25a4ba 100644
--- a/source/opt/local_single_block_elim_pass.cpp
+++ b/source/opt/local_single_block_elim_pass.cpp
@@ -292,6 +292,7 @@ void LocalSingleBlockLoadStoreElimPass::InitExtensions() {
                                 "SPV_EXT_shader_atomic_float_add",
                                 "SPV_EXT_fragment_shader_interlock",
                                 "SPV_NV_compute_shader_derivatives",
+                                "SPV_NV_cooperative_matrix",
                                 "SPV_KHR_cooperative_matrix"});
 }
 
diff --git a/source/opt/local_single_store_elim_pass.cpp b/source/opt/local_single_store_elim_pass.cpp
index aa7a756955..7dfc4adfc8 100644
--- a/source/opt/local_single_store_elim_pass.cpp
+++ b/source/opt/local_single_store_elim_pass.cpp
@@ -142,6 +142,7 @@ void LocalSingleStoreElimPass::InitExtensionAllowList() {
                                 "SPV_EXT_shader_atomic_float_add",
                                 "SPV_EXT_fragment_shader_interlock",
                                 "SPV_NV_compute_shader_derivatives",
+                                "SPV_NV_cooperative_matrix",
                                 "SPV_KHR_cooperative_matrix"});
 }
 bool LocalSingleStoreElimPass::ProcessVariable(Instruction* var_inst) {
diff --git a/source/opt/mem_pass.cpp b/source/opt/mem_pass.cpp
index 6e59bf0f8d..80ec8da18e 100644
--- a/source/opt/mem_pass.cpp
+++ b/source/opt/mem_pass.cpp
@@ -43,6 +43,7 @@ bool MemPass::IsBaseTargetType(const Instruction* typeInst) const {
     case spv::Op::OpTypeSampler:
     case spv::Op::OpTypeSampledImage:
     case spv::Op::OpTypePointer:
+    case spv::Op::OpTypeCooperativeMatrixNV:
     case spv::Op::OpTypeCooperativeMatrixKHR:
       return true;
     default: