diff --git a/src/common/gsvector.cpp b/src/common/gsvector.cpp
index 787fb7d66..c62da4d8a 100644
--- a/src/common/gsvector.cpp
+++ b/src/common/gsvector.cpp
@@ -87,25 +87,25 @@ GSMatrix4x4::GSMatrix4x4(float e00, float e01, float e02, float e03, float e10,
   E[3][3] = e33;
 }
 
- GSMatrix4x4::GSMatrix4x4(const GSMatrix2x2& m)
+GSMatrix4x4::GSMatrix4x4(const GSMatrix2x2& m)
 {
-   E[0][0] = m.E[0][0];
-   E[0][1] = m.E[0][1];
-   E[0][2] = 0.0f;
-   E[0][3] = 0.0f;
-   E[1][0] = m.E[1][0];
-   E[1][1] = m.E[1][1];
-   E[1][2] = 0.0f;
-   E[1][3] = 0.0f;
-   E[2][0] = 0.0f;
-   E[2][1] = 0.0f;
-   E[2][2] = 1.0f;
-   E[2][3] = 0.0f;
-   E[3][0] = 0.0f;
-   E[3][1] = 0.0f;
-   E[3][2] = 0.0f;
-   E[3][3] = 1.0f;
- }
+  E[0][0] = m.E[0][0];
+  E[0][1] = m.E[0][1];
+  E[0][2] = 0.0f;
+  E[0][3] = 0.0f;
+  E[1][0] = m.E[1][0];
+  E[1][1] = m.E[1][1];
+  E[1][2] = 0.0f;
+  E[1][3] = 0.0f;
+  E[2][0] = 0.0f;
+  E[2][1] = 0.0f;
+  E[2][2] = 1.0f;
+  E[2][3] = 0.0f;
+  E[3][0] = 0.0f;
+  E[3][1] = 0.0f;
+  E[3][2] = 0.0f;
+  E[3][3] = 1.0f;
+}
 
 GSMatrix4x4 GSMatrix4x4::operator*(const GSMatrix4x4& m) const
 {
@@ -136,12 +136,41 @@ GSMatrix4x4 GSMatrix4x4::operator*(const GSMatrix4x4& m) const
   return res;
 }
 
+GSMatrix4x4& GSMatrix4x4::operator*=(const GSMatrix4x4& m)
+{
+  const GSMatrix4x4 copy(*this);
+
+#define MultRC(rw, cl)                                                                                                 \
+  copy.E[rw][0] * m.E[0][cl] + copy.E[rw][1] * m.E[1][cl] + copy.E[rw][2] * m.E[2][cl] + copy.E[rw][3] * m.E[3][cl]
+
+  E[0][0] = MultRC(0, 0);
+  E[0][1] = MultRC(0, 1);
+  E[0][2] = MultRC(0, 2);
+  E[0][3] = MultRC(0, 3);
+  E[1][0] = MultRC(1, 0);
+  E[1][1] = MultRC(1, 1);
+  E[1][2] = MultRC(1, 2);
+  E[1][3] = MultRC(1, 3);
+  E[2][0] = MultRC(2, 0);
+  E[2][1] = MultRC(2, 1);
+  E[2][2] = MultRC(2, 2);
+  E[2][3] = MultRC(2, 3);
+  E[3][0] = MultRC(3, 0);
+  E[3][1] = MultRC(3, 1);
+  E[3][2] = MultRC(3, 2);
+  E[3][3] = MultRC(3, 3);
+
+#undef MultRC
+
+  return *this;
+}
+
 GSVector4 GSMatrix4x4::operator*(const GSVector4& v) const
 {
   const GSVector4 r0 = row(0);
   const GSVector4 r1 = row(1);
   const GSVector4 r2 = row(2);
-  const GSVector4 r3 = row(4);
+  const GSVector4 r3 = row(3);
 
   return GSVector4(r0.dot(v), r1.dot(v), r2.dot(v), r3.dot(v));
 }
@@ -199,6 +228,11 @@ GSMatrix4x4 GSMatrix4x4::RotationZ(float angle_in_radians)
                      0.0f, 0.0f, 1.0f);
 }
 
+GSMatrix4x4 GSMatrix4x4::Translation(float x, float y, float z)
+{
+  return GSMatrix4x4(1.0f, 0.0f, 0.0f, x, 0.0f, 1.0f, 0.0f, y, 0.0f, 0.0f, 1.0f, z, 0.0f, 0.0f, 0.0f, 1.0f);
+}
+
 GSMatrix4x4 GSMatrix4x4::OffCenterOrthographicProjection(float left, float top, float right, float bottom, float zNear,
                                                          float zFar)
 {
@@ -222,6 +256,61 @@ GSVector4 GSMatrix4x4::col(size_t i) const
   return GSVector4(E[0][i], E[1][i], E[2][i], E[3][i]);
 }
 
+GSMatrix4x4 GSMatrix4x4::Invert() const
+{
+  GSMatrix4x4 ret;
+
+  float v0 = E[2][0] * E[3][1] - E[2][1] * E[3][0];
+  float v1 = E[2][0] * E[3][2] - E[2][2] * E[3][0];
+  float v2 = E[2][0] * E[3][3] - E[2][3] * E[3][0];
+  float v3 = E[2][1] * E[3][2] - E[2][2] * E[3][1];
+  float v4 = E[2][1] * E[3][3] - E[2][3] * E[3][1];
+  float v5 = E[2][2] * E[3][3] - E[2][3] * E[3][2];
+
+  const float t00 = +(v5 * E[1][1] - v4 * E[1][2] + v3 * E[1][3]);
+  const float t10 = -(v5 * E[1][0] - v2 * E[1][2] + v1 * E[1][3]);
+  const float t20 = +(v4 * E[1][0] - v2 * E[1][1] + v0 * E[1][3]);
+  const float t30 = -(v3 * E[1][0] - v1 * E[1][1] + v0 * E[1][2]);
+
+  const float inv_det = 1.0f / (t00 * E[0][0] + t10 * E[0][1] + t20 * E[0][2] + t30 * E[0][3]);
+
+  ret.E[0][0] = t00 * inv_det;
+  ret.E[1][0] = t10 * inv_det;
+  ret.E[2][0] = t20 * inv_det;
+  ret.E[3][0] = t30 * inv_det;
+
+  ret.E[0][1] = -(v5 * E[0][1] - v4 * E[0][2] + v3 * E[0][3]) * inv_det;
+  ret.E[1][1] = +(v5 * E[0][0] - v2 * E[0][2] + v1 * E[0][3]) * inv_det;
+  ret.E[2][1] = -(v4 * E[0][0] - v2 * E[0][1] + v0 * E[0][3]) * inv_det;
+  ret.E[3][1] = +(v3 * E[0][0] - v1 * E[0][1] + v0 * E[0][2]) * inv_det;
+
+  v0 = E[1][0] * E[3][1] - E[1][1] * E[3][0];
+  v1 = E[1][0] * E[3][2] - E[1][2] * E[3][0];
+  v2 = E[1][0] * E[3][3] - E[1][3] * E[3][0];
+  v3 = E[1][1] * E[3][2] - E[1][2] * E[3][1];
+  v4 = E[1][1] * E[3][3] - E[1][3] * E[3][1];
+  v5 = E[1][2] * E[3][3] - E[1][3] * E[3][2];
+
+  ret.E[0][2] = +(v5 * E[0][1] - v4 * E[0][2] + v3 * E[0][3]) * inv_det;
+  ret.E[1][2] = -(v5 * E[0][0] - v2 * E[0][2] + v1 * E[0][3]) * inv_det;
+  ret.E[2][2] = +(v4 * E[0][0] - v2 * E[0][1] + v0 * E[0][3]) * inv_det;
+  ret.E[3][2] = -(v3 * E[0][0] - v1 * E[0][1] + v0 * E[0][2]) * inv_det;
+
+  v0 = E[2][1] * E[1][0] - E[2][0] * E[1][1];
+  v1 = E[2][2] * E[1][0] - E[2][0] * E[1][2];
+  v2 = E[2][3] * E[1][0] - E[2][0] * E[1][3];
+  v3 = E[2][2] * E[1][1] - E[2][1] * E[1][2];
+  v4 = E[2][3] * E[1][1] - E[2][1] * E[1][3];
+  v5 = E[2][3] * E[1][2] - E[2][2] * E[1][3];
+
+  ret.E[0][3] = -(v5 * E[0][1] - v4 * E[0][2] + v3 * E[0][3]) * inv_det;
+  ret.E[1][3] = +(v5 * E[0][0] - v2 * E[0][2] + v1 * E[0][3]) * inv_det;
+  ret.E[2][3] = -(v4 * E[0][0] - v2 * E[0][1] + v0 * E[0][3]) * inv_det;
+  ret.E[3][3] = +(v3 * E[0][0] - v1 * E[0][1] + v0 * E[0][2]) * inv_det;
+
+  return ret;
+}
+
 void GSMatrix4x4::store(void* m)
 {
   std::memcpy(m, &E[0][0], sizeof(E));
diff --git a/src/common/gsvector.h b/src/common/gsvector.h
index 106e29b35..4a3b1306c 100644
--- a/src/common/gsvector.h
+++ b/src/common/gsvector.h
@@ -47,6 +47,7 @@ public:
   GSMatrix4x4(const GSMatrix2x2& m);
 
   GSMatrix4x4 operator*(const GSMatrix4x4& m) const;
+  GSMatrix4x4& operator*=(const GSMatrix4x4& m);
 
   GSVector4 operator*(const GSVector4& v) const;
 
@@ -55,6 +56,7 @@ public:
   static GSMatrix4x4 RotationX(float angle_in_radians);
   static GSMatrix4x4 RotationY(float angle_in_radians);
   static GSMatrix4x4 RotationZ(float angle_in_radians);
+  static GSMatrix4x4 Translation(float x, float y, float z);
 
   static GSMatrix4x4 OffCenterOrthographicProjection(float left, float top, float right, float bottom, float zNear,
                                                      float zFar);
@@ -63,6 +65,8 @@ public:
   GSVector4 row(size_t i) const;
   GSVector4 col(size_t i) const;
 
+  GSMatrix4x4 Invert() const;
+
   void store(void* m);
 
   float E[4][4];