diff --git a/sycl/test-e2e/Matrix/Inputs/joint_matrix_out_bounds_impl.hpp b/sycl/test-e2e/Matrix/Inputs/joint_matrix_out_bounds_impl.hpp
index fef7bf0bda74..92ae22103d49 100644
--- a/sycl/test-e2e/Matrix/Inputs/joint_matrix_out_bounds_impl.hpp
+++ b/sycl/test-e2e/Matrix/Inputs/joint_matrix_out_bounds_impl.hpp
@@ -20,6 +20,7 @@ void matrix_multiply(T1 *C, T2 *A, T2 *B, queue q) {
   size_t NDRangeM = M / TM + (((M % TM) != 0) ? 1 : 0);
   size_t NDRangeN = N / TN;
   size_t sg_size = get_sg_size<mult<K, B_layout, vnniFactor>>(q);
+  std::cout << "SG size: " << sg_size << " ";
 
   q.submit([&](handler &cgh) {
      cgh.parallel_for<mult<K, B_layout, vnniFactor>>(
@@ -109,21 +110,31 @@ void test() {
   matrix_multiply_ref(A, B, D, MATRIX_M, MATRIX_N, MATRIX_K);
 
   // test data
-  if constexpr (A_layout == layout::row_major) {
-    if constexpr (B_layout == layout::row_major) {
-      matrix_multiply<Tc, Tab, MATRIX_M, MATRIX_N, MATRIX_K, TM, TN, TK,
-                      A_layout, B_layout, vnniFactor>(C, A, B, q);
-    } else if constexpr (B_layout == layout::col_major) {
-    } else {
-      Tab *vnniB = malloc_shared<Tab>(MATRIX_K * MATRIX_N, q);
-      matrix_vnni<Tab>(MATRIX_K, MATRIX_N, B, vnniB, vnniFactor);
-      matrix_multiply<Tc, Tab, MATRIX_M, MATRIX_N, MATRIX_K, TM, TN, TK,
-                      A_layout, B_layout, vnniFactor>(C, A, vnniB, q);
-      free(vnniB, q);
-    }
-  } else {
+  if constexpr (A_layout == layout::col_major) {
+    Tab *colA = malloc_shared<Tab>(MATRIX_K * MATRIX_M, q);
+    matrix_transpose(MATRIX_M, MATRIX_K, colA, A);
+    Tab *tmp = A;
+    A = colA;
+    free(tmp, q);
   }
 
+  if constexpr (B_layout == layout::col_major) {
+    Tab *colB = malloc_shared<Tab>(MATRIX_N * MATRIX_K, q);
+    matrix_transpose(MATRIX_K, MATRIX_N, colB, B);
+    Tab *tmp = B;
+    B = colB;
+    free(tmp, q);
+  }
+
+  if constexpr (B_layout == layout::ext_intel_packed) {
+    Tab *vnniB = malloc_shared<Tab>(MATRIX_K * MATRIX_N, q);
+    matrix_vnni(MATRIX_K, MATRIX_N, B, vnniB, vnniFactor);
+    Tab *tmp = B;
+    B = vnniB;
+    free(tmp, q);
+  }
+
+  matrix_multiply<Tc, Tab, MATRIX_M, MATRIX_N, MATRIX_K, TM, TN, TK, A_layout, B_layout, vnniFactor>(C, A, B, q);
   assert(matrix_compare(MATRIX_M, MATRIX_N, C, D));
   std::cout << "passed" << std::endl;
 
diff --git a/sycl/test-e2e/Matrix/joint_matrix_out_bounds.cpp b/sycl/test-e2e/Matrix/joint_matrix_out_bounds.cpp
index dbc33017b0a6..72f172f16be9 100644
--- a/sycl/test-e2e/Matrix/joint_matrix_out_bounds.cpp
+++ b/sycl/test-e2e/Matrix/joint_matrix_out_bounds.cpp
@@ -16,15 +16,18 @@
 #include "joint_matrix_out_bounds_impl.hpp"
 
 int main() {
-  std::cout << "bf16:\n";
+  std::cout << "bf16 A row major, B row major: ";
   test<bfloat16, float, 1024 + 14, 1024, 1024 + 24, 8, 16, 16,
        layout::row_major, layout::row_major, 1>();
+  std::cout << "bf16 A row major, B packed: ";
   test<bfloat16, float, 1024 + 14, 1024, 1024 + 24, 8, 16, 16,
        layout::row_major, layout::ext_intel_packed, 2>();
 
   // unaligned k:
+  std::cout << "bf16 A row major, B row major: ";
   test<bfloat16, float, 1024 + 14, 1024, 1024 + 14, 8, 16, 16,
        layout::row_major, layout::row_major, 1>();
+  std::cout << "bf16 A row major, B packed: ";
   test<bfloat16, float, 1024 + 14, 1024, 1024 + 14, 8, 16, 16,
        layout::row_major, layout::ext_intel_packed, 2>();
 }
diff --git a/sycl/test-e2e/Matrix/joint_matrix_out_bounds_colmajor.cpp b/sycl/test-e2e/Matrix/joint_matrix_out_bounds_colmajor.cpp
new file mode 100644
index 000000000000..531a4d0bf160
--- /dev/null
+++ b/sycl/test-e2e/Matrix/joint_matrix_out_bounds_colmajor.cpp
@@ -0,0 +1,44 @@
+//==-------- joint_matrix_out_bounds.cpp  - DPC++ joint_matrix--------------==//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// REQUIRES: aspect-ext_intel_matrix
+// UNSUPPORTED: gpu-intel-dg2, cpu
+
+// RUN: %{build} -o %t.out
+// RUN: %{run} %t.out
+
+// RUN: %{build} -o %t32.out -DSG_SZ=32
+// RUN: %{run} %t32.out
+
+// XFAIL:gpu
+// XFAIL-TRACKER: GSD-5768
+
+#include "common.hpp"
+#include "joint_matrix_out_bounds_impl.hpp"
+
+int main() {
+  std::cout << "bf16 A col major, B col major: ";
+  test<bfloat16, float, 1024 + 14, 1024, 1024 + 24, 8, 16, 16,
+       layout::col_major, layout::col_major, 1>();
+  std::cout << "half A col major, B col major: ";
+  test<half, float, 1024 + 14, 1024, 1024 + 24, 8, 16, 16,
+       layout::col_major, layout::col_major, 1>();
+  std::cout << "int8 A col major, B col major: ";
+  test<int8_t, int32_t, 1024 + 14, 1024, 1024 + 24, 8, 16, 32,
+       layout::col_major, layout::col_major, 2>();
+
+  // unaligned k:
+  std::cout << "bf16 A col major, B col major: ";
+  test<bfloat16, float, 1024 + 14, 1024, 1024 + 14, 8, 16, 16,
+       layout::col_major, layout::col_major, 1>();
+  std::cout << "half A col major, B col major: ";
+  test<half, float, 1024 + 14, 1024, 1024 + 14, 8, 16, 16,
+       layout::col_major, layout::col_major, 1>();
+  std::cout << "int8 A col major, B col major: ";
+  test<int8_t, int32_t, 1024 + 14, 1024, 1024 + 14, 8, 16, 32,
+       layout::col_major, layout::col_major, 2>();
+}