diff --git a/libs/math/Matrix3.h b/libs/math/Matrix3.h
index d01bb42055..4d4721e18b 100644
--- a/libs/math/Matrix3.h
+++ b/libs/math/Matrix3.h
@@ -1,5 +1,6 @@
 #pragma once
 
+#include "Vector2.h"
 #include "Vector3.h"
 #include "eigen.h"
 
@@ -126,6 +127,59 @@ class alignas(16) Matrix3
     static Matrix3 byRows(double xx, double yx, double zx,
         double xy, double yy, double zy,
         double xz, double yz, double zz);
+
+    /// Return the result of this matrix post-multiplied by another matrix.
+    Matrix3 getMultipliedBy(const Matrix3& other) const
+    {
+        return Matrix3(_transform * other.eigen());
+    }
+
+    /// Post-multiply this matrix by another matrix, in-place.
+    void multiplyBy(const Matrix3& other)
+    {
+        *this = getMultipliedBy(other);
+    }
+
+    /// Returns this matrix pre-multiplied by the other
+    Matrix3 getPremultipliedBy(const Matrix3& other) const
+    {
+        return other.getMultipliedBy(*this);
+    }
+
+    /// Pre-multiplies this matrix by other in-place.
+    void premultiplyBy(const Matrix3& other)
+    {
+        *this = getPremultipliedBy(other);
+    }
+
+    /// Return the full inverse of this matrix.
+    Matrix3 getFullInverse() const
+    {
+        return Matrix3(_transform.inverse(Eigen::Projective));
+    }
+
+    /// Invert this matrix in-place.
+    void invertFull()
+    {
+        *this = getFullInverse();
+    }
+
+    /**
+     * \brief Returns the given 2-component point transformed by this matrix.
+     *
+     * The point is assumed to have a W component of 1, and no division by W is
+     * performed before returning the 3-component vector.
+     */
+    template<typename T>
+    BasicVector2<T> transformPoint(const BasicVector2<T>& point) const
+    {
+        auto transformed = transform(BasicVector3<T>(point.x(), point.y(), 1));
+        return BasicVector2<T>(transformed.x(), transformed.y());
+    }
+
+    /// Return the given 3-component vector transformed by this matrix.
+    template<typename T>
+    BasicVector3<T> transform(const BasicVector3<T>& vector3) const;
 };
 
 // Private constructor
@@ -164,6 +218,14 @@ inline Matrix3 Matrix3::byRows(double xx, double yx, double zx,
         zx, zy, zz);
 }
 
+template<typename T>
+BasicVector3<T> Matrix3::transform(const BasicVector3<T>& vector3) const
+{
+    Eigen::Matrix<T, 3, 1> eVec(static_cast<const double*>(vector3));
+    auto result = _transform * eVec;
+    return BasicVector3<T>(result[0], result[1], result[2]);
+}
+
 /// Compare two matrices elementwise for equality
 inline bool operator==(const Matrix3& l, const Matrix3& r)
 {
@@ -175,3 +237,32 @@ inline bool operator!=(const Matrix3& l, const Matrix3& r)
 {
     return !(l == r);
 }
+
+/// Multiply two matrices together
+inline Matrix3 operator*(const Matrix3& m1, const Matrix3& m2)
+{
+    return m1.getMultipliedBy(m2);
+}
+
+/**
+ * \brief Multiply a 3-component vector by this matrix.
+ *
+ * Equivalent to m.transform(v).
+ */
+template<typename T>
+BasicVector3<T> operator*(const Matrix3& m, const BasicVector3<T>& v)
+{
+    return m.transform(v);
+}
+
+/**
+ * \brief Multiply a 2-component vector by this matrix.
+ *
+ * The vector is upgraded to a 3-component vector with a Z (or W) component of 1, i.e.
+ * equivalent to m.transformPoint(v).
+ */
+template<typename T>
+BasicVector2<T> operator*(const Matrix3& m, const BasicVector2<T>& v)
+{
+    return m.transformPoint(v);
+}
diff --git a/test/math/Matrix3.cpp b/test/math/Matrix3.cpp
index f7a5b0853c..bd18db511d 100644
--- a/test/math/Matrix3.cpp
+++ b/test/math/Matrix3.cpp
@@ -87,4 +87,71 @@ TEST(Matrix3Test, MatrixEquality)
     EXPECT_TRUE(m2 != Matrix3::getIdentity());
 }
 
+TEST(Matrix3Test, MatrixMultiplication)
+{
+    auto a = Matrix3::byColumns(3, 5, 7, 11, 13, 17, 19, 23, 29);
+    auto b = Matrix3::byColumns(61, 67, 71, 73, 79, 83, 89, 97, 101);
+
+    // Check multiplied result
+    auto c = a.getMultipliedBy(b);
+    EXPECT_EQ(c, Matrix3::byColumns(2269, 2809, 3625,
+        2665, 3301, 4261,
+        3253, 4029, 5201));
+
+    // Multiplication has not changed original
+    EXPECT_NE(a, c);
+
+    // Check operator multiplication as well
+    EXPECT_EQ(a * b, c);
+
+    // Test Pre-Multiplication
+    EXPECT_EQ(b.getMultipliedBy(a), a.getPremultipliedBy(b)) << "Matrix pre-multiplication mismatch";
+}
+
+TEST(Matrix3Test, MatrixFullInverse)
+{
+    auto a = Matrix3::byColumns(3, 5, 7, 11, 13, 17, 19, 23, 29);
+
+    auto inv = a.getFullInverse();
+
+    EXPECT_DOUBLE_EQ(inv.xx(), -7.0 / 10) << "Matrix inversion failed on xx";
+    EXPECT_DOUBLE_EQ(inv.xy(), 4.0 / 5) << "Matrix inversion failed on xy";
+    EXPECT_DOUBLE_EQ(inv.xz(), -3.0 / 10) << "Matrix inversion failed on xz";
+
+    EXPECT_DOUBLE_EQ(inv.yx(), 1.0 / 5) << "Matrix inversion failed on yx";
+    EXPECT_DOUBLE_EQ(inv.yy(), -23.0 / 10) << "Matrix inversion failed on yy";
+    EXPECT_DOUBLE_EQ(inv.yz(), 13.0 / 10) << "Matrix inversion failed on yz";
+
+    EXPECT_DOUBLE_EQ(inv.zx(), 3.0 / 10) << "Matrix inversion failed on zx";
+    EXPECT_DOUBLE_EQ(inv.zy(), 13.0 / 10) << "Matrix inversion failed on zy";
+    EXPECT_DOUBLE_EQ(inv.zz(), -4.0 / 5) << "Matrix inversion failed on zz";
+}
+
+TEST(Matrix3Test, MatrixTransformation)
+{
+    auto a = Matrix3::byColumns(3, 5, 7, 11, 13, 17, 19, 23, 29);
+
+    {
+        Vector2 v(61, 67);
+
+        Vector2 transformed = a.transformPoint(v);
+
+        EXPECT_EQ(transformed.x(), 939) << "Vector2 transformation failed";
+        EXPECT_EQ(transformed.y(), 1199) << "Vector2 transformation failed";
+
+        EXPECT_EQ(a * v, a.transformPoint(v));
+    }
+
+    {
+        Vector3 vector(83, 89, 97);
+        Vector3 transformed = a.transform(vector);
+
+        EXPECT_EQ(transformed.x(), 3071) << "Vector3 transformation failed";
+        EXPECT_EQ(transformed.y(), 3803) << "Vector3 transformation failed";
+        EXPECT_EQ(transformed.z(), 4907) << "Vector3 transformation failed";
+
+        EXPECT_EQ(a * vector, a.transform(vector));
+    }
+}
+
 }