diff --git a/mlir/lib/IR/OperationSupport.cpp b/mlir/lib/IR/OperationSupport.cpp
--- a/mlir/lib/IR/OperationSupport.cpp
+++ b/mlir/lib/IR/OperationSupport.cpp
@@ -633,8 +633,18 @@
       op->getName(), op->getAttrDictionary(), op->getResultTypes());
 
   //   - Operands
-  for (Value operand : op->getOperands())
-    hash = llvm::hash_combine(hash, hashOperands(operand));
+  if (op->hasTrait<mlir::OpTrait::IsCommutative>()) {
+    llvm::SmallVector<void *> vec;
+    for (auto i = op->operand_begin(), e = op->operand_end(); i != e; ++i)
+      vec.push_back((*i).getAsOpaquePointer());
+    llvm::sort(vec.begin(), vec.end());
+    hash = llvm::hash_combine(hash,
+                              llvm::hash_combine_range(vec.begin(), vec.end()));
+  } else {
+    for (Value operand : op->getOperands())
+      hash = llvm::hash_combine(hash, hashOperands(operand));
+  }
+
   //   - Operands
   for (Value result : op->getResults())
     hash = llvm::hash_combine(hash, hashResults(result));
@@ -723,10 +733,23 @@
         }
         return true;
       };
-  // Check mapping of operands and results.
-  if (!checkValueRangeMapping(lhs->getOperands(), rhs->getOperands(),
-                              mapOperands))
-    return false;
+  if (lhs->hasTrait<mlir::OpTrait::IsCommutative>()) {
+    SmallVector<void *> lops;
+    for (auto lod : lhs->getOperands())
+      lops.push_back(lod.getAsOpaquePointer());
+    llvm::sort(lops.begin(), lops.end());
+    SmallVector<void *> rops;
+    for (auto rod : rhs->getOperands())
+      rops.push_back(rod.getAsOpaquePointer());
+    llvm::sort(rops.begin(), rops.end());
+    if (!std::equal(lops.begin(), lops.end(), rops.begin()))
+      return false;
+  } else {
+    // Check mapping of operands and results.
+    if (!checkValueRangeMapping(lhs->getOperands(), rhs->getOperands(),
+                                mapOperands))
+      return false;
+  }
   if (!checkValueRangeMapping(lhs->getResults(), rhs->getResults(), mapResults))
     return false;
   for (auto regionPair : llvm::zip(lhs->getRegions(), rhs->getRegions()))
diff --git a/mlir/test/Transforms/cse.mlir b/mlir/test/Transforms/cse.mlir
--- a/mlir/test/Transforms/cse.mlir
+++ b/mlir/test/Transforms/cse.mlir
@@ -310,3 +310,15 @@
   %2 = arith.addi %0, %1 : i32
   return %2 : i32
 }
+
+/// This test is checking that identical commutative operation are gracefully
+/// handled but the CSE pass.
+// CHECK-LABEL: func @check_cummutative_cse
+func @check_cummutative_cse(%a : i32, %b : i32) -> i32 {
+  // CHECK: %[[ADD1:.*]] = arith.addi %{{.*}}, %{{.*}} : i32
+  %1 = arith.addi %a, %b : i32
+  %2 = arith.addi %b, %a : i32
+  // CHECK-NEXT:  arith.muli %[[ADD1]], %[[ADD1]] : i32
+  %3 = arith.muli %1, %2 : i32
+  return %3 : i32
+}