diff --git a/llvm/lib/Transforms/Scalar/LowerMatrixIntrinsics.cpp b/llvm/lib/Transforms/Scalar/LowerMatrixIntrinsics.cpp
index ab16ec77be10..60619dbe2f58 100644
--- a/llvm/lib/Transforms/Scalar/LowerMatrixIntrinsics.cpp
+++ b/llvm/lib/Transforms/Scalar/LowerMatrixIntrinsics.cpp
@@ -804,9 +804,10 @@ public:
                        m_Value(TA), m_ConstantInt(R), m_ConstantInt(C))))
       return nullptr;
 
-    // Transpose of a transpose is a nop
+    // Transpose of a transpose is a nop when the shapes match.
     Value *TATA;
-    if (match(TA, m_Intrinsic<Intrinsic::matrix_transpose>(m_Value(TATA)))) {
+    if (match(TA, m_Intrinsic<Intrinsic::matrix_transpose>(
+                      m_Value(TATA), m_Specific(C), m_Specific(R)))) {
       updateShapeAndReplaceAllUsesWith(I, TATA);
       eraseFromParentAndMove(&I, II, BB);
       eraseFromParentAndMove(TA, II, BB);
diff --git a/llvm/test/Transforms/LowerMatrixIntrinsics/transpose-fold.ll b/llvm/test/Transforms/LowerMatrixIntrinsics/transpose-fold.ll
new file mode 100644
index 000000000000..ef2e224f69c5
--- /dev/null
+++ b/llvm/test/Transforms/LowerMatrixIntrinsics/transpose-fold.ll
@@ -0,0 +1,35 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 5
+; RUN: opt -passes='lower-matrix-intrinsics' -S < %s | FileCheck %s
+
+; We can only fold matching transposes.
+
+define void @reshape(ptr %in, ptr %out) {
+; CHECK-LABEL: define void @reshape(
+; CHECK-SAME: ptr [[IN:%.*]], ptr [[OUT:%.*]]) {
+; CHECK-NEXT:  [[ENTRY:.*:]]
+; CHECK-NEXT:    [[COL_LOAD:%.*]] = load <4 x double>, ptr [[IN]], align 8
+; CHECK-NEXT:    [[SPLIT:%.*]] = shufflevector <4 x double> [[COL_LOAD]], <4 x double> poison, <2 x i32> <i32 0, i32 1>
+; CHECK-NEXT:    [[SPLIT1:%.*]] = shufflevector <4 x double> [[COL_LOAD]], <4 x double> poison, <2 x i32> <i32 2, i32 3>
+; CHECK-NEXT:    [[TMP0:%.*]] = extractelement <2 x double> [[SPLIT]], i64 0
+; CHECK-NEXT:    [[TMP1:%.*]] = insertelement <2 x double> poison, double [[TMP0]], i64 0
+; CHECK-NEXT:    [[TMP2:%.*]] = extractelement <2 x double> [[SPLIT1]], i64 0
+; CHECK-NEXT:    [[TMP3:%.*]] = insertelement <2 x double> [[TMP1]], double [[TMP2]], i64 1
+; CHECK-NEXT:    [[TMP4:%.*]] = extractelement <2 x double> [[SPLIT]], i64 1
+; CHECK-NEXT:    [[TMP5:%.*]] = insertelement <2 x double> poison, double [[TMP4]], i64 0
+; CHECK-NEXT:    [[TMP6:%.*]] = extractelement <2 x double> [[SPLIT1]], i64 1
+; CHECK-NEXT:    [[TMP7:%.*]] = insertelement <2 x double> [[TMP5]], double [[TMP6]], i64 1
+; CHECK-NEXT:    store <2 x double> [[TMP3]], ptr [[OUT]], align 8
+; CHECK-NEXT:    [[VEC_GEP:%.*]] = getelementptr double, ptr [[OUT]], i64 2
+; CHECK-NEXT:    store <2 x double> [[TMP7]], ptr [[VEC_GEP]], align 8
+; CHECK-NEXT:    ret void
+;
+entry:
+  %0 = load <4 x double>, ptr %in, align 8
+  %1 = tail call <4 x double> @llvm.matrix.transpose.v4f64(<4 x double> %0, i32 4, i32 1)
+  %2 = tail call <4 x double> @llvm.matrix.transpose.v4f64(<4 x double> %1, i32 1, i32 4)
+  %3 = tail call <4 x double> @llvm.matrix.transpose.v4f64(<4 x double> %2, i32 2, i32 2)
+  %4 = tail call <4 x double> @llvm.matrix.transpose.v4f64(<4 x double> %3, i32 2, i32 2)
+  %5 = tail call <4 x double> @llvm.matrix.transpose.v4f64(<4 x double> %4, i32 2, i32 2)
+  store <4 x double> %5, ptr %out, align 8
+  ret void
+}