diff --git a/sycl/include/CL/__spirv/spirv_types.hpp b/sycl/include/CL/__spirv/spirv_types.hpp
index cae0f38c11748..4fb0fa8886796 100644
--- a/sycl/include/CL/__spirv/spirv_types.hpp
+++ b/sycl/include/CL/__spirv/spirv_types.hpp
@@ -108,11 +108,32 @@ enum class GroupOperation : uint32_t {
   ExclusiveScan = 2
 };
 
-enum class MatrixLayout { RowMajor, ColumnMajor, PackedA, PackedB };
+enum class MatrixLayout : uint32_t {
+  RowMajor = 0,
+  ColumnMajor = 1,
+  PackedA = 2,
+  PackedB = 3
+};
 
+// TODO: replace the following W/A with a better solution when we have it.
+// The following structure is used to represent the joint matrix type in the
+// LLVM IR. The structure has a pointer to a multidimensional array member which
+// makes the encoding of the matrix type information within the LLVM IR looks
+// like this:
+// %struct.__spirv_JointMatrixINTEL = type { [42 x [6 x [2 x [1 x float]]]]* }
+// Note that an array cannot be of zero size but MatrixLayout and Scope
+// parameters can; hence '+ 1' is added to the 3rd and 4th dimensions.
+// In general, representing a matrix type information like this is a bit odd
+// (especially for MatrixLayout and Scope parameters). But with the current
+// tools we have in Clang, this is the only way to preserve and communicate this
+// information to SPIRV translator.
+// The long term solution would be to introduce a matrix type in Clang and use
+// it instead of this member.
 template <typename T, std::size_t R, std::size_t C, MatrixLayout U,
           Scope::Flag S = Scope::Flag::Subgroup>
-struct __spirv_JointMatrixINTEL;
+struct __spirv_JointMatrixINTEL {
+  T (*Value)[R][C][static_cast<size_t>(U) + 1][static_cast<size_t>(S) + 1];
+};
 
 } // namespace __spv
 
diff --git a/sycl/test/matrix/matrix-int8-test.cpp b/sycl/test/matrix/matrix-int8-test.cpp
index a1fce823e12a1..ba4327a8e6cd5 100644
--- a/sycl/test/matrix/matrix-int8-test.cpp
+++ b/sycl/test/matrix/matrix-int8-test.cpp
@@ -1,5 +1,9 @@
-// RUN: %clangxx -fsycl -O2 %s -o %t.out
-// XFAIL: *
+// RUN: %clangxx -fsycl -fsycl-device-only -O2 -S -emit-llvm -o - %s | FileCheck %s
+
+// CHECK-DAG: %"struct.__spv::__spirv_JointMatrixINTEL" = type { [12 x [48 x [1 x [4 x i8]]]] addrspace(4)* }
+// CHECK-DAG: %"struct.__spv::__spirv_JointMatrixINTEL.[[#]]" = type { [12 x [12 x [1 x [4 x i32]]]] addrspace(4)* }
+// CHECK-DAG: %"struct.__spv::__spirv_JointMatrixINTEL.[[#]]" = type { [48 x [12 x [4 x [4 x i8]]]] addrspace(4)* }
+
 #include <CL/sycl.hpp>
 #if (SYCL_EXT_ONEAPI_MATRIX == 2)
 #include <iostream>