diff --git a/src/api/math.lua b/src/api/math.lua
index fc7fb18d..a9f46b34 100644
--- a/src/api/math.lua
+++ b/src/api/math.lua
@@ -266,7 +266,7 @@ ffi.metatype(mat4, {
         m.m[0], m.m[1], m.m[2], m.m[3],
         m.m[4], m.m[5], m.m[6], m.m[7],
         m.m[8], m.m[9], m.m[10], m.m[11],
-        m.m[12], m.m[13], m.m[14], m.m[15] = ...
+        m.m[12], m.m[13], m.m[14], m.m[15] = x, ...
       end
       return m
     end,
@@ -283,21 +283,19 @@ ffi.metatype(mat4, {
 
     identity = function(m)
       checkmat4(m)
-      C.mat4_identity(m)
+      return C.mat4_identity(m)
     end,
 
-    inverse = function(m)
+    invert = function(m, out)
       checkmat4(m)
-      local out = math.mat4()
-      C.mat4_invert(C.mat4_set(out, m))
-      return out
+      out = out and C.mat4_set(out, m) or m
+      return C.mat4_invert(out)
     end,
 
     transpose = function(m)
       checkmat4(m)
-      local out = math.mat4()
-      C.mat4_transpose(C.mat4_set(out, m))
-      return out
+      out = out and C.mat4_set(out, m) or m
+      return C.mat4_transpose(out)
     end,
 
     translate = function(m, x, y, z)
@@ -368,5 +366,9 @@ ffi.metatype(mat4, {
       C.mat4_transform(m, f + 0, f + 1, f + 2)
       return math.vec3(f[0], f[1], f[2])
     end
+  end,
+
+  __tostring = function(m)
+    return 'mat4'
   end
 })
diff --git a/src/api/math.lua.h b/src/api/math.lua.h
index b61921b4..54d7bf4a 100644
--- a/src/api/math.lua.h
+++ b/src/api/math.lua.h
@@ -647,215 +647,218 @@ unsigned char math_lua[] = {
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 };
-unsigned int math_lua_len = 10287;
+unsigned int math_lua_len = 10332;
diff --git a/src/api/types/mat4.c b/src/api/types/mat4.c
index 4bb87325..41e477c8 100644
--- a/src/api/types/mat4.c
+++ b/src/api/types/mat4.c
@@ -100,19 +100,19 @@ static int l_lovrMat4Identity(lua_State* L) {
   return 1;
 }
 
-static int l_lovrMat4Inverse(lua_State* L) {
+static int l_lovrMat4Invert(lua_State* L) {
   mat4 m = luax_checkmathtype(L, 1, MATH_MAT4, NULL);
-  mat4 n = lovrPoolAllocate(lovrMathGetPool(), MATH_MAT4);
-  mat4_invert(mat4_init(n, m));
-  luax_pushlightmathtype(L, n, MATH_MAT4);
+  mat4 out = lua_gettop(L) > 1 ? mat4_init(luax_checkmathtype(L, 2, MATH_MAT4, NULL), m) : m;
+  mat4_invert(out);
+  luax_pushlightmathtype(L, out, MATH_MAT4);
   return 1;
 }
 
 static int l_lovrMat4Transpose(lua_State* L) {
   mat4 m = luax_checkmathtype(L, 1, MATH_MAT4, NULL);
-  mat4 n = lovrPoolAllocate(lovrMathGetPool(), MATH_MAT4);
-  mat4_transpose(mat4_init(n, m));
-  luax_pushlightmathtype(L, n, MATH_MAT4);
+  mat4 out = lua_gettop(L) > 1 ? mat4_init(luax_checkmathtype(L, 2, MATH_MAT4, NULL), m) : m;
+  mat4_transpose(out);
+  luax_pushlightmathtype(L, out, MATH_MAT4);
   return 1;
 }
 
@@ -220,13 +220,19 @@ static int l_lovrMat4__mul(lua_State* L) {
   return 1;
 }
 
+static int l_lovrMat4__tostring(lua_State* L) {
+  mat4 m = luax_checkmathtype(L, 1, MATH_MAT4, NULL);
+  lua_pushliteral(L, "mat4");
+  return 1;
+}
+
 const luaL_Reg lovrMat4[] = {
   { "unpack", l_lovrMat4Unpack },
   { "set", l_lovrMat4Set },
   { "copy", l_lovrMat4Copy },
   { "save", l_lovrMat4Save },
   { "identity", l_lovrMat4Identity },
-  { "inverse", l_lovrMat4Inverse },
+  { "invert", l_lovrMat4Invert },
   { "transpose", l_lovrMat4Transpose },
   { "translate", l_lovrMat4Translate },
   { "rotate", l_lovrMat4Rotate },
@@ -236,5 +242,6 @@ const luaL_Reg lovrMat4[] = {
   { "perspective", l_lovrMat4Perspective },
   { "orthographic", l_lovrMat4Orthographic },
   { "__mul", l_lovrMat4__mul },
+  { "__tostring", l_lovrMat4__tostring },
   { NULL, NULL }
 };