diff --git a/src/Avalonia.Base/Utilities/MathUtilities.cs b/src/Avalonia.Base/Utilities/MathUtilities.cs
index 042e7f84c6..d4d2bf16b8 100644
--- a/src/Avalonia.Base/Utilities/MathUtilities.cs
+++ b/src/Avalonia.Base/Utilities/MathUtilities.cs
@@ -1,5 +1,4 @@
 using System;
-using System.Runtime.InteropServices;
 
 namespace Avalonia.Utilities
 {
diff --git a/src/Avalonia.Visuals/Matrix.cs b/src/Avalonia.Visuals/Matrix.cs
index e18140aa8d..3c8e5e39f2 100644
--- a/src/Avalonia.Visuals/Matrix.cs
+++ b/src/Avalonia.Visuals/Matrix.cs
@@ -9,6 +9,8 @@ namespace Avalonia
     /// </summary>
     public readonly struct Matrix : IEquatable<Matrix>
     {
+        private const float DecomposeEpsilon = 0.0001f;
+
         private readonly double _m11;
         private readonly double _m12;
         private readonly double _m21;
@@ -54,7 +56,7 @@ namespace Avalonia
         /// <summary>
         /// HasInverse Property - returns true if this matrix is invertible, false otherwise.
         /// </summary>
-        public bool HasInverse => GetDeterminant() != 0;
+        public bool HasInverse => Math.Abs(GetDeterminant()) >= double.Epsilon;
 
         /// <summary>
         /// The first element of the first row
@@ -286,7 +288,7 @@ namespace Avalonia
         {
             double d = GetDeterminant();
 
-            if (d == 0)
+            if (Math.Abs(d) < double.Epsilon)
             {
                 throw new InvalidOperationException("Transform is not invertible.");
             }
@@ -325,8 +327,9 @@ namespace Avalonia
             decomposed = default;
 
             var determinant = matrix.GetDeterminant();
-
-            if (determinant == 0)
+            
+            // Based upon constant in System.Numerics.Matrix4x4.
+            if (Math.Abs(determinant) < DecomposeEpsilon)
             {
                 return false;
             }
diff --git a/tests/Avalonia.Benchmarks/Visuals/MatrixBenchmarks.cs b/tests/Avalonia.Benchmarks/Visuals/MatrixBenchmarks.cs
new file mode 100644
index 0000000000..17e2237eb0
--- /dev/null
+++ b/tests/Avalonia.Benchmarks/Visuals/MatrixBenchmarks.cs
@@ -0,0 +1,16 @@
+using BenchmarkDotNet.Attributes;
+
+namespace Avalonia.Benchmarks.Visuals
+{
+    [MemoryDiagnoser, InProcess]
+    public class MatrixBenchmarks
+    {
+        private static readonly Matrix s_data = Matrix.Identity;
+
+        [Benchmark(Baseline = true)]
+        public bool Decompose()
+        {
+            return Matrix.TryDecomposeTransform(s_data, out Matrix.Decomposed decomposed);
+        }
+    }
+}
diff --git a/tests/Avalonia.Visuals.UnitTests/Media/MatrixTests.cs b/tests/Avalonia.Visuals.UnitTests/Media/MatrixTests.cs
index 44e2e8663b..6ef48b6161 100644
--- a/tests/Avalonia.Visuals.UnitTests/Media/MatrixTests.cs
+++ b/tests/Avalonia.Visuals.UnitTests/Media/MatrixTests.cs
@@ -1,4 +1,4 @@
-using System.Globalization;
+using System;
 using Avalonia.Utilities;
 using Xunit;
 
@@ -7,13 +7,29 @@ namespace Avalonia.Visuals.UnitTests.Media
     public class MatrixTests
     {
         [Fact]
-        public void Parse_Parses()
+        public void Can_Parse()
         {
             var matrix = Matrix.Parse("1,2,3,-4,5 6");
             var expected = new Matrix(1, 2, 3, -4, 5, 6);
             Assert.Equal(expected, matrix);
         }
 
+        [Fact]
+        public void Singular_Has_No_Inverse()
+        {
+            var matrix = new Matrix(0, 0, 0, 0, 0, 0);
+
+            Assert.False(matrix.HasInverse);
+        }
+
+        [Fact]
+        public void Identity_Has_Inverse()
+        {
+            var matrix = Matrix.Identity;
+
+            Assert.True(matrix.HasInverse);
+        }
+
         [Fact]
         public void Can_Decompose_Translation()
         {
@@ -26,17 +42,25 @@ namespace Avalonia.Visuals.UnitTests.Media
             Assert.Equal(10, decomposed.Translate.Y);
         }
 
-        [Fact]
-        public void Can_Decompose_Angle()
+        [Theory]
+        [InlineData(30d)]
+        [InlineData(0d)]
+        [InlineData(90d)]
+        [InlineData(270d)]
+        public void Can_Decompose_Angle(double angleDeg)
         {
-            var angleRad = MathUtilities.Deg2Rad(30);
+            var angleRad = MathUtilities.Deg2Rad(angleDeg);
 
             var matrix = Matrix.CreateRotation(angleRad);
 
             var result = Matrix.TryDecomposeTransform(matrix, out Matrix.Decomposed decomposed);
 
             Assert.Equal(true, result);
-            Assert.Equal(angleRad, decomposed.Angle);
+
+            var expected = NormalizeAngle(angleRad);
+            var actual = NormalizeAngle(decomposed.Angle);
+
+            Assert.Equal(expected, actual, 4);
         }
 
         [Theory]
@@ -54,5 +78,22 @@ namespace Avalonia.Visuals.UnitTests.Media
             Assert.Equal(x, decomposed.Scale.X);
             Assert.Equal(y, decomposed.Scale.Y);
         }
+
+        private static double NormalizeAngle(double rad)
+        {
+            double twoPi = 2 * Math.PI;
+
+            while (rad < 0)
+            {
+                rad += twoPi;
+            }
+
+            while (rad > twoPi)
+            {
+                rad -= twoPi;
+            }
+
+            return rad;
+        }
     }
 }