diff --git a/renderdoc/driver/shaders/spirv/spirv_debug.cpp b/renderdoc/driver/shaders/spirv/spirv_debug.cpp
index ef3d5e6e7..11775c8e4 100644
--- a/renderdoc/driver/shaders/spirv/spirv_debug.cpp
+++ b/renderdoc/driver/shaders/spirv/spirv_debug.cpp
@@ -1455,6 +1455,21 @@ void ThreadState::StepNext(ShaderDebugState *state, const rdcarray<ThreadState>
       SetDst(state, mul.result, var);
       break;
     }
+    case Op::Transpose:
+    {
+      OpTranspose transpose(it);
+
+      ShaderVariable matrix = GetSrc(transpose.matrix);
+      ShaderVariable var = matrix;
+      std::swap(var.rows, var.columns);
+
+      for(uint8_t r = 0; r < var.rows; r++)
+        for(uint8_t c = 0; c < var.columns; c++)
+          var.value.fv[r * var.columns + c] = matrix.value.fv[c * matrix.columns + r];
+
+      SetDst(state, transpose.result, var);
+      break;
+    }
     case Op::MatrixTimesVector:
     {
       OpMatrixTimesVector mul(it);
diff --git a/renderdoc/driver/shaders/spirv/spirv_debug_glsl450.cpp b/renderdoc/driver/shaders/spirv/spirv_debug_glsl450.cpp
index f18389138..62f9eaae3 100644
--- a/renderdoc/driver/shaders/spirv/spirv_debug_glsl450.cpp
+++ b/renderdoc/driver/shaders/spirv/spirv_debug_glsl450.cpp
@@ -24,6 +24,7 @@
 
 #include "spirv_debug.h"
 #include <math.h>
+#include "maths/matrix.h"
 
 namespace rdcspv
 {
@@ -179,6 +180,67 @@ ShaderVariable Pow(ThreadState &state, const rdcarray<Id> &params)
   return var;
 }
 
+ShaderVariable Determinant(ThreadState &state, const rdcarray<Id> &params)
+{
+  CHECK_PARAMS(1);
+
+  ShaderVariable m = state.GetSrc(params[0]);
+
+  RDCASSERTEQUAL(m.rows, m.columns);
+
+  if(m.rows == 4)
+  {
+    Matrix4f mat;
+    mat.SetFrom(m.value.fv);
+    m.value.f.x = mat.Determinant();
+  }
+  else if(m.rows == 3)
+  {
+    Matrix3f mat;
+    mat.SetFrom(m.value.fv);
+    m.value.f.x = mat.Determinant();
+  }
+  else if(m.rows == 2)
+  {
+    Matrix2f mat;
+    mat.SetFrom(m.value.fv);
+    m.value.f.x = mat.Determinant();
+  }
+  m.rows = m.columns = 1;
+
+  return m;
+}
+
+ShaderVariable MatrixInverse(ThreadState &state, const rdcarray<Id> &params)
+{
+  CHECK_PARAMS(1);
+
+  ShaderVariable m = state.GetSrc(params[0]);
+
+  RDCASSERTEQUAL(m.rows, m.columns);
+
+  if(m.rows == 4)
+  {
+    Matrix4f mat;
+    mat.SetFrom(m.value.fv);
+    memcpy(m.value.fv, mat.Inverse().Data(), sizeof(mat));
+  }
+  else if(m.rows == 3)
+  {
+    Matrix3f mat;
+    mat.SetFrom(m.value.fv);
+    memcpy(m.value.fv, mat.Inverse().Data(), sizeof(mat));
+  }
+  else if(m.rows == 2)
+  {
+    Matrix2f mat;
+    mat.SetFrom(m.value.fv);
+    memcpy(m.value.fv, mat.Inverse().Data(), sizeof(mat));
+  }
+
+  return m;
+}
+
 template <typename T>
 static T GLSLMax(T x, T y)
 {
@@ -457,6 +519,8 @@ void ConfigureGLSLStd450(ExtInstDispatcher &extinst)
   EXT(Ceil);
   EXT(Fract);
   EXT(Pow);
+  EXT(Determinant);
+  EXT(MatrixInverse);
   EXT(FMin);
   EXT(UMin);
   EXT(SMin);
diff --git a/renderdoc/maths/matrix.cpp b/renderdoc/maths/matrix.cpp
index 61d21c81e..f3e12bb03 100644
--- a/renderdoc/maths/matrix.cpp
+++ b/renderdoc/maths/matrix.cpp
@@ -31,11 +31,6 @@
 #include "quat.h"
 #include "vec.h"
 
-static inline size_t matIdx(const size_t x, const size_t y)
-{
-  return x + y * 4;
-}
-
 Matrix4f Matrix4f::Mul(const Matrix4f &o) const
 {
   Matrix4f m;
@@ -62,6 +57,24 @@ Matrix4f Matrix4f::Transpose() const
   return m;
 }
 
+float Matrix4f::Determinant() const
+{
+  float a0 = (*this)[0] * (*this)[5] - (*this)[1] * (*this)[4];
+  float a1 = (*this)[0] * (*this)[6] - (*this)[2] * (*this)[4];
+  float a2 = (*this)[0] * (*this)[7] - (*this)[3] * (*this)[4];
+  float a3 = (*this)[1] * (*this)[6] - (*this)[2] * (*this)[5];
+  float a4 = (*this)[1] * (*this)[7] - (*this)[3] * (*this)[5];
+  float a5 = (*this)[2] * (*this)[7] - (*this)[3] * (*this)[6];
+  float b0 = (*this)[8] * (*this)[13] - (*this)[9] * (*this)[12];
+  float b1 = (*this)[8] * (*this)[14] - (*this)[10] * (*this)[12];
+  float b2 = (*this)[8] * (*this)[15] - (*this)[11] * (*this)[12];
+  float b3 = (*this)[9] * (*this)[14] - (*this)[10] * (*this)[13];
+  float b4 = (*this)[9] * (*this)[15] - (*this)[11] * (*this)[13];
+  float b5 = (*this)[10] * (*this)[15] - (*this)[11] * (*this)[14];
+
+  return a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0;
+}
+
 Matrix4f Matrix4f::Inverse() const
 {
   float a0 = (*this)[0] * (*this)[5] - (*this)[1] * (*this)[4];
@@ -120,7 +133,7 @@ Matrix4f Matrix4f::Inverse() const
   }
 
   // no inverse
-  return Matrix4f::Identity();
+  return Matrix4f::Zero();
 }
 
 Vec3f Matrix4f::Transform(const Vec3f &v, const float w) const
@@ -274,3 +287,77 @@ Matrix4f Matrix4f::ReversePerspective(const float degfov, const float N, const f
 
   return Matrix4f(persp);
 }
+
+Matrix3f Matrix3f::Transpose() const
+{
+  Matrix3f m;
+  for(size_t x = 0; x < 3; x++)
+    for(size_t y = 0; y < 3; y++)
+      m[matIdx(x, y)] = (*this)[matIdx(y, x)];
+
+  return m;
+}
+
+float Matrix3f::Determinant() const
+{
+  return f[0] * (f[4] * f[8] - f[5] * f[7]) - f[1] * (f[3] * f[8] - f[5] * f[6]) +
+         f[2] * (f[3] * f[7] - f[4] * f[6]);
+}
+
+Matrix3f Matrix3f::Inverse() const
+{
+  float det = Determinant();
+  Matrix3f m = {};
+  if(fabsf(det) > FLT_EPSILON)
+  {
+    m[0] = Matrix2f(f[matIdx(1, 1)], f[matIdx(2, 1)], f[matIdx(1, 2)], f[matIdx(2, 2)]).Determinant();
+    m[1] = Matrix2f(f[matIdx(1, 0)], f[matIdx(2, 0)], f[matIdx(1, 2)], f[matIdx(2, 2)]).Determinant();
+    m[2] = Matrix2f(f[matIdx(1, 0)], f[matIdx(2, 0)], f[matIdx(1, 1)], f[matIdx(2, 1)]).Determinant();
+
+    m[3] = Matrix2f(f[matIdx(0, 1)], f[matIdx(2, 1)], f[matIdx(0, 2)], f[matIdx(2, 2)]).Determinant();
+    m[4] = Matrix2f(f[matIdx(0, 0)], f[matIdx(2, 0)], f[matIdx(0, 2)], f[matIdx(2, 2)]).Determinant();
+    m[5] = Matrix2f(f[matIdx(0, 0)], f[matIdx(2, 0)], f[matIdx(0, 1)], f[matIdx(2, 1)]).Determinant();
+
+    m[6] = Matrix2f(f[matIdx(0, 1)], f[matIdx(1, 1)], f[matIdx(0, 2)], f[matIdx(1, 2)]).Determinant();
+    m[7] = Matrix2f(f[matIdx(0, 0)], f[matIdx(1, 0)], f[matIdx(0, 2)], f[matIdx(1, 2)]).Determinant();
+    m[8] = Matrix2f(f[matIdx(0, 0)], f[matIdx(1, 0)], f[matIdx(0, 1)], f[matIdx(1, 1)]).Determinant();
+
+    float invdet = 1.0f / Determinant();
+
+    for(size_t i = 0; i < 9; i++)
+    {
+      m[i] *= invdet;
+      if(i & 1)
+        m[i] *= -1.0f;
+    }
+  }
+  return m;
+}
+
+Matrix2f Matrix2f::Transpose() const
+{
+  Matrix2f m = *this;
+  m[1] = f[2];
+  m[2] = f[1];
+  return m;
+}
+
+float Matrix2f::Determinant() const
+{
+  return f[0] * f[3] - f[1] * f[2];
+}
+
+Matrix2f Matrix2f::Inverse() const
+{
+  float det = Determinant();
+  Matrix2f m = {};
+  if(fabsf(det) > FLT_EPSILON)
+  {
+    float invdet = 1.0f / Determinant();
+    m[0] = invdet * f[3];
+    m[1] = invdet * -f[1];
+    m[2] = invdet * -f[2];
+    m[3] = invdet * f[0];
+  }
+  return m;
+}
diff --git a/renderdoc/maths/matrix.h b/renderdoc/maths/matrix.h
index 81cbd6196..9a406303a 100644
--- a/renderdoc/maths/matrix.h
+++ b/renderdoc/maths/matrix.h
@@ -65,12 +65,14 @@ public:
   inline float operator[](const size_t i) const { return f[i]; }
   inline float &operator[](const size_t i) { return f[i]; }
   Matrix4f Transpose() const;
+  float Determinant() const;
   Matrix4f Inverse() const;
   Matrix4f Mul(const Matrix4f &o) const;
 
   Vec3f Transform(const Vec3f &v, const float w = 1.0f) const;
 
   const float *Data() const { return &f[0]; }
+  void SetFrom(float data[16]) { memcpy(f, data, sizeof(Matrix4f)); }
   const Vec3f GetPosition() const;
   const Vec3f GetForward() const;
   const Vec3f GetRight() const;
@@ -80,5 +82,47 @@ private:
   Matrix4f(const float *d) { memcpy(f, d, sizeof(Matrix4f)); }
   friend class Quatf;
 
+  constexpr inline size_t matIdx(const size_t x, const size_t y) const { return x + y * 4; }
   float f[16];
 };
+
+class Matrix3f
+{
+public:
+  Matrix3f() {}
+  inline float operator[](const size_t i) const { return f[i]; }
+  inline float &operator[](const size_t i) { return f[i]; }
+  Matrix3f Transpose() const;
+  float Determinant() const;
+  Matrix3f Inverse() const;
+
+  const float *Data() const { return &f[0]; }
+  void SetFrom(float data[9]) { memcpy(f, data, sizeof(Matrix3f)); }
+private:
+  constexpr inline size_t matIdx(const size_t x, const size_t y) const { return x + y * 3; }
+  float f[9];
+};
+
+class Matrix2f
+{
+public:
+  Matrix2f() {}
+  Matrix2f(float a, float b, float c, float d)
+  {
+    f[0] = a;
+    f[1] = b;
+    f[2] = c;
+    f[3] = d;
+  }
+  inline float operator[](const size_t i) const { return f[i]; }
+  inline float &operator[](const size_t i) { return f[i]; }
+  Matrix2f Transpose() const;
+  float Determinant() const;
+  Matrix2f Inverse() const;
+
+  const float *Data() const { return &f[0]; }
+  void SetFrom(float data[4]) { memcpy(f, data, sizeof(Matrix2f)); }
+private:
+  constexpr inline size_t matIdx(const size_t x, const size_t y) const { return x + y * 2; }
+  float f[4];
+};
diff --git a/util/test/demos/vk/vk_shader_debug_zoo.cpp b/util/test/demos/vk/vk_shader_debug_zoo.cpp
index b222ee15d..7096b5578 100644
--- a/util/test/demos/vk/vk_shader_debug_zoo.cpp
+++ b/util/test/demos/vk/vk_shader_debug_zoo.cpp
@@ -953,6 +953,23 @@ void main()
 
         %_vec = OpCompositeConstruct %float4 %randf_16 %randf_17 %randf_18 %randf_19
 
+ %_out_float4 = OpMatrixTimesVector %float4 %_mat %_vec
+)EOTEST",
+        R"EOTEST(
+       %_cola = OpCompositeConstruct %float4 %randf_0 %randf_1 %randf_2 %randf_3
+       %_colb = OpCompositeConstruct %float4 %randf_4 %randf_5 %randf_6 %randf_7
+       %_mat1 = OpCompositeConstruct %float4x2 %_cola %_colb
+
+       %_colc = OpCompositeConstruct %float4 %randf_8 %randf_9 %randf_10 %randf_11
+       %_cold = OpCompositeConstruct %float4 %randf_12 %randf_13 %randf_14 %randf_15
+       %_mat2 = OpCompositeConstruct %float4x2 %_colc %_cold
+
+      %_mat2t = OpTranspose %float2x4 %_mat2
+
+        %_mat = OpMatrixTimesMatrix %float4x4 %_mat1 %_mat2t
+
+        %_vec = OpCompositeConstruct %float4 %randf_16 %randf_17 %randf_18 %randf_19
+
  %_out_float4 = OpMatrixTimesVector %float4 %_mat %_vec
 )EOTEST",
         R"EOTEST(
@@ -968,9 +985,76 @@ void main()
         R"EOTEST(
         %_vec = OpCompositeConstruct %float4 %randf_0 %randf_1 %randf_2 %randf_3
  %_out_float4 = OpVectorTimesScalar %float4 %_vec %randf_4
+)EOTEST",
+        R"EOTEST(
+       %_cola = OpCompositeConstruct %float2 %randf_0 %randf_1
+       %_colb = OpCompositeConstruct %float2 %randf_4 %randf_5
+       %_colc = OpCompositeConstruct %float2 %randf_8 %randf_9
+       %_cold = OpCompositeConstruct %float2 %randf_12 %randf_13
+       %_mat1 = OpCompositeConstruct %float2x2 %_cola %_colb
+
+  %_out_float = OpExtInst %float %glsl450 Determinant %_mat1
+)EOTEST",
+        R"EOTEST(
+       %_cola = OpCompositeConstruct %float3 %randf_0 %randf_1 %randf_2
+       %_colb = OpCompositeConstruct %float3 %randf_4 %randf_5 %randf_6
+       %_colc = OpCompositeConstruct %float3 %randf_8 %randf_9 %randf_10
+       %_mat1 = OpCompositeConstruct %float3x3 %_cola %_colb %_colc
+
+  %_out_float = OpExtInst %float %glsl450 Determinant %_mat1
+)EOTEST",
+        R"EOTEST(
+       %_cola = OpCompositeConstruct %float4 %randf_0 %randf_1 %randf_2 %randf_3
+       %_colb = OpCompositeConstruct %float4 %randf_4 %randf_5 %randf_6 %randf_7
+       %_colc = OpCompositeConstruct %float4 %randf_8 %randf_9 %randf_10 %randf_11
+       %_cold = OpCompositeConstruct %float4 %randf_12 %randf_13 %randf_14 %randf_15
+       %_mat1 = OpCompositeConstruct %float4x4 %_cola %_colb %_colc %_cold
+
+  %_out_float = OpExtInst %float %glsl450 Determinant %_mat1
 )EOTEST",
     });
 
+    // test matrix inverse, but round the result to avoid needing to lower our global precision
+    // epsilon
+    for(int dim = 2; dim <= 4; dim++)
+    {
+      std::string test = fmt::format(R"EOTEST(
+       %_cola = OpCompositeConstruct %float{0} %randf_0 %randf_1 {1} %randf_2 {2} %randf_3
+       %_colb = OpCompositeConstruct %float{0} %randf_4 %randf_5 {1} %randf_6 {2} %randf_7
+       %_colc = OpCompositeConstruct %float{0} %randf_8 %randf_9 {1} %randf_10 {2} %randf_11
+       %_cold = OpCompositeConstruct %float{0} %randf_12 %randf_13 {1} %randf_14 {2} %randf_15
+
+        %_mat = OpCompositeConstruct %float{0}x{0} %_cola %_colb {1} %_colc {2} %_cold
+
+        %_vec = OpCompositeConstruct %float{0} %randf_16 %randf_17 {1} %randf_18 {2} %randf_19
+
+       %_mat0 = OpExtInst %float{0}x{0} %glsl450 MatrixInverse %_mat
+)EOTEST",
+                                     dim, dim < 3 ? ";" : "", dim < 4 ? ";" : "");
+
+      int i = 0;
+      for(int col = 0; col < dim; col++)
+      {
+        for(int row = 0; row < dim; row++)
+        {
+          test += fmt::format(R"EOTEST(
+     %_mat{0}{1}a = OpCompositeExtract %float %_mat{2} {0} {1}
+     %_mat{0}{1}b = OpFMul %float %_mat{0}{1}a %float_500_0
+     %_mat{0}{1}c = OpExtInst %float %glsl450 RoundEven %_mat{0}{1}b
+     %_mat{0}{1}d = OpFDiv %float %_mat{0}{1}c %float_500_0
+
+         %_mat{3} = OpCompositeInsert %float{4}x{4} %_mat{0}{1}d %_mat{2} {0} {1}
+)EOTEST",
+                              col, row, i, i + 1, dim);
+          i++;
+        }
+      }
+
+      test += fmt::format("%_out_float{0} = OpMatrixTimesVector %float{0} %_mat{1} %_vec\n", dim, i);
+
+      asm_tests.push_back(test);
+    }
+
     // test OpVectorShuffle
     append_tests({
         "%_out_float4 = OpVectorShuffle %float4 %float4_0000 %float4_1234 7 6 0 1",
@@ -1347,6 +1431,7 @@ void main()
      %uint4 = OpTypeVector %uint 4
 
    %float2x2 = OpTypeMatrix %float2 2
+   %float3x3 = OpTypeMatrix %float3 3
    %float2x4 = OpTypeMatrix %float2 4
    %float4x2 = OpTypeMatrix %float4 2
    %float4x4 = OpTypeMatrix %float4 4