diff --git a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
index 22d5afcd77381..309079e549846 100644
--- a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
+++ b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVArithmeticOps.td
@@ -23,7 +23,7 @@ class SPIRV_ArithmeticBinaryOp<string mnemonic, Type type,
       // Operands type same as result type.
       SPIRV_BinaryOp<mnemonic, type, type,
                    !listconcat(traits,
-                               [Pure, SameOperandsAndResultType])> {
+                               [Pure, AllTypesMatch<["operand1", "operand2", "result"]>])> {
   // In addition to normal types arithmetic instructions can support cooperative
   // matrix.
   let arguments = (ins
@@ -42,7 +42,7 @@ class SPIRV_ArithmeticUnaryOp<string mnemonic, Type type,
       // Operand type same as result type.
       SPIRV_UnaryOp<mnemonic, type, type,
                    !listconcat(traits,
-                               [Pure, SameOperandsAndResultType])> {
+                               [Pure, AllTypesMatch<["operand", "result"]>])> {
   // In addition to normal types arithmetic instructions can support cooperative
   // matrix.
   let arguments = (ins
diff --git a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVTypes.h b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVTypes.h
index 2e29e9afaabf4..787535d0a6bd2 100644
--- a/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVTypes.h
+++ b/mlir/include/mlir/Dialect/SPIRV/IR/SPIRVTypes.h
@@ -394,7 +394,8 @@ hash_value(const StructType::MemberDecorationInfo &memberDecorationInfo);
 // SPIR-V KHR cooperative matrix type
 class CooperativeMatrixType
     : public Type::TypeBase<CooperativeMatrixType, CompositeType,
-                            detail::CooperativeMatrixTypeStorage> {
+                            detail::CooperativeMatrixTypeStorage,
+                            ShapedType::Trait> {
 public:
   using Base::Base;
 
@@ -418,6 +419,22 @@ class CooperativeMatrixType
                      std::optional<StorageClass> storage = std::nullopt);
   void getCapabilities(SPIRVType::CapabilityArrayRefVector &capabilities,
                        std::optional<StorageClass> storage = std::nullopt);
+
+  operator ShapedType() const { return llvm::cast<ShapedType>(*this); }
+
+  ArrayRef<int64_t> getShape() const;
+
+  bool hasRank() const { return true; }
+
+  CooperativeMatrixType cloneWith(std::optional<ArrayRef<int64_t>> shape,
+                                  Type elementType) const {
+    if (!shape)
+      return get(elementType, getRows(), getColumns(), getScope(), getUse());
+
+    assert(shape.value().size() == 2);
+    return get(elementType, shape.value()[0], shape.value()[1], getScope(),
+               getUse());
+  }
 };
 
 // SPIR-V matrix type
diff --git a/mlir/lib/Dialect/SPIRV/IR/SPIRVTypes.cpp b/mlir/lib/Dialect/SPIRV/IR/SPIRVTypes.cpp
index 337df3a5a65f0..1aff43c301334 100644
--- a/mlir/lib/Dialect/SPIRV/IR/SPIRVTypes.cpp
+++ b/mlir/lib/Dialect/SPIRV/IR/SPIRVTypes.cpp
@@ -194,8 +194,21 @@ std::optional<int64_t> CompositeType::getSizeInBytes() {
 //===----------------------------------------------------------------------===//
 
 struct spirv::detail::CooperativeMatrixTypeStorage final : TypeStorage {
+  // In the specification dimensions of the Cooperative Matrix are 32-bit
+  // integers --- the initial implementation kept those values as such. However,
+  // the `ShapedType` expects the shape to be `int64_t`. We could keep the shape
+  // as 32-bits and expose it as int64_t through `getShape`, however, this
+  // method returns an `ArrayRef`, so returning `ArrayRef<int64_t>` having two
+  // 32-bits integers would require an extra logic and storage. So, we diverge
+  // from the spec and internally represent the dimensions as 64-bit integers,
+  // so we can easily return an `ArrayRef` from `getShape` without any extra
+  // logic. Alternatively, we could store both rows and columns (both 32-bits)
+  // and shape (64-bits), assigning rows and columns to shape whenever
+  // `getShape` is called. This would be at the cost of extra logic and storage.
+  // Note: Because `ArrayRef` is returned we cannot construct an object in
+  // `getShape` on the fly.
   using KeyTy =
-      std::tuple<Type, uint32_t, uint32_t, Scope, CooperativeMatrixUseKHR>;
+      std::tuple<Type, int64_t, int64_t, Scope, CooperativeMatrixUseKHR>;
 
   static CooperativeMatrixTypeStorage *
   construct(TypeStorageAllocator &allocator, const KeyTy &key) {
@@ -204,17 +217,17 @@ struct spirv::detail::CooperativeMatrixTypeStorage final : TypeStorage {
   }
 
   bool operator==(const KeyTy &key) const {
-    return key == KeyTy(elementType, rows, columns, scope, use);
+    return key == KeyTy(elementType, shape[0], shape[1], scope, use);
   }
 
   CooperativeMatrixTypeStorage(const KeyTy &key)
-      : elementType(std::get<0>(key)), rows(std::get<1>(key)),
-        columns(std::get<2>(key)), scope(std::get<3>(key)),
+      : elementType(std::get<0>(key)),
+        shape({std::get<1>(key), std::get<2>(key)}), scope(std::get<3>(key)),
         use(std::get<4>(key)) {}
 
   Type elementType;
-  uint32_t rows;
-  uint32_t columns;
+  // [#rows, #columns]
+  std::array<int64_t, 2> shape;
   Scope scope;
   CooperativeMatrixUseKHR use;
 };
@@ -231,10 +244,18 @@ Type CooperativeMatrixType::getElementType() const {
   return getImpl()->elementType;
 }
 
-uint32_t CooperativeMatrixType::getRows() const { return getImpl()->rows; }
+uint32_t CooperativeMatrixType::getRows() const {
+  assert(getImpl()->shape[0] != ShapedType::kDynamic);
+  return static_cast<uint32_t>(getImpl()->shape[0]);
+}
 
 uint32_t CooperativeMatrixType::getColumns() const {
-  return getImpl()->columns;
+  assert(getImpl()->shape[1] != ShapedType::kDynamic);
+  return static_cast<uint32_t>(getImpl()->shape[1]);
+}
+
+ArrayRef<int64_t> CooperativeMatrixType::getShape() const {
+  return getImpl()->shape;
 }
 
 Scope CooperativeMatrixType::getScope() const { return getImpl()->scope; }
diff --git a/mlir/test/Dialect/SPIRV/IR/khr-cooperative-matrix-ops.mlir b/mlir/test/Dialect/SPIRV/IR/khr-cooperative-matrix-ops.mlir
index d3e1dbc229ef9..8733ff93768ab 100644
--- a/mlir/test/Dialect/SPIRV/IR/khr-cooperative-matrix-ops.mlir
+++ b/mlir/test/Dialect/SPIRV/IR/khr-cooperative-matrix-ops.mlir
@@ -524,7 +524,7 @@ spirv.func @matrix_times_scalar(%a: !matA_f32, %b: f32) "None" {
 
 spirv.func @iadd(%a: !spirv.coopmatrix<2x2xi32, Subgroup, MatrixA>,
                  %b: !spirv.coopmatrix<2x2xi32, Subgroup, MatrixB>) "None" {
-  // expected-error @+1 {{op requires the same type for all operands and results}}
+  // expected-error @+1 {{failed to verify that all of {operand1, operand2, result} have same type}}
   %q = "spirv.IAdd"(%a, %b) :
     (!spirv.coopmatrix<2x2xi32, Subgroup, MatrixA>, !spirv.coopmatrix<2x2xi32, Subgroup, MatrixB>)
     -> !spirv.coopmatrix<2x2xi32, Subgroup, MatrixA>
@@ -535,7 +535,7 @@ spirv.func @iadd(%a: !spirv.coopmatrix<2x2xi32, Subgroup, MatrixA>,
 
 spirv.func @fadd(%a: !spirv.coopmatrix<2x2xf32, Subgroup, MatrixA>,
                  %b: !spirv.coopmatrix<2x2xf32, Subgroup, MatrixAcc>) "None" {
-  // expected-error @+1 {{op requires the same type for all operands and results}}
+  // expected-error @+1 {{failed to verify that all of {operand1, operand2, result} have same type}}
   %q = "spirv.FAdd"(%a, %b) :
     (!spirv.coopmatrix<2x2xf32, Subgroup, MatrixA>, !spirv.coopmatrix<2x2xf32, Subgroup, MatrixAcc>)
     -> !spirv.coopmatrix<2x2xf32, Subgroup, MatrixAcc>