diff --git a/docs/source/mat2x3.rst b/docs/source/mat2x3.rst
index 433c637..06780d6 100644
--- a/docs/source/mat2x3.rst
+++ b/docs/source/mat2x3.rst
@@ -23,6 +23,16 @@ Functions:
 #. :c:func:`glm_mat2x3_transpose`
 #. :c:func:`glm_mat2x3_scale`
 
+Represented
+~~~~~~~~~~~
+
+.. csv-table:: mat2x3
+   :header: "", "column 1", "column 2"
+
+   "row 1", "m00", "m10"
+   "row 2", "m01", "m11"
+   "row 3", "m02", "m12"
+
 Functions documentation
 ~~~~~~~~~~~~~~~~~~~~~~~
 
@@ -51,28 +61,68 @@ Functions documentation
       | *[in]*  **src**  pointer to an array of floats
       | *[out]* **dest** destination matrix2x3
 
-.. c:function:: void glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest)
+.. c:function:: void glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat3 dest)
 
     multiply m1 and m2 to dest
 
     .. code-block:: c
 
-       glm_mat2x3_mul(mat2x3, mat3x2, mat2);
+       glm_mat2x3_mul(mat2x3, mat3x2, mat3);
 
     Parameters:
       | *[in]*  **m1**    left matrix (mat2x3)
       | *[in]*  **m2**    right matrix (mat3x2)
-      | *[out]* **dest**  destination matrix (mat2)
+      | *[out]* **dest**  destination matrix (mat3)
 
-.. c:function:: void glm_mat2x3_mulv(mat2x3 m, vec3 v, vec2 dest)
+    .. csv-table:: mat2x3
+        :header: "", "column 1", "column 2"
 
-    multiply mat2x3 with vec3 (column vector) and store in dest vector
+        "row 1", "a00", "a10"
+        "row 2", "a01", "a11"
+        "row 3", "a02", "a12"
+
+    .. csv-table:: mat3x2
+        :header: "", "column 1", "column 2", "column 3"
+
+        "row 1", "b00", "b10", "b20"
+        "row 2", "b01", "b11", "b21"
+
+    .. csv-table:: mat3x3
+        :header: "", "column 1", "column 2", "column 3"
+
+        "row 1", "a00 * b00 + a10 * b01", "a00 * b10 + a10 * b11", "a00 * b20 + a10 * b21"
+        "row 2", "a01 * b00 + a11 * b01", "a01 * b10 + a11 * b11", "a01 * b20 + a11 * b21"
+        "row 3", "a02 * b00 + a12 * b01", "a02 * b10 + a12 * b11", "a02 * b20 + a12 * b21"
+
+.. c:function:: void glm_mat2x3_mulv(mat2x3 m, vec2 v, vec3 dest)
+
+    multiply mat2x3 with vec2 (column vector) and store in dest column vector
 
     Parameters:
       | *[in]*  **m**     mat2x3 (left)
       | *[in]*  **v**     vec3 (right, column vector)
       | *[out]* **dest**  destination (result, column vector)
 
+    .. csv-table:: mat2x3
+        :header: "", "column 1", "column 2"
+
+        "row 1", "m00", "m10"
+        "row 2", "m01", "m11"
+        "row 3", "m02", "m12"
+
+    .. csv-table:: column vec2 (1x2)
+        :header: "", "column 1"
+
+        "row 1", "v0"
+        "row 2", "v1"
+
+    .. csv-table:: column vec3 (1x3)
+        :header: "", "column 1"
+
+        "row 1", "m00 * v0 + m10 * v1"
+        "row 2", "m01 * v0 + m11 * v1"
+        "row 3", "m02 * v0 + m12 * v1"
+
 .. c:function:: void glm_mat2x3_transpose(mat2x3 m, mat3x2 dest)
 
     transpose matrix and store in dest
diff --git a/include/cglm/call/mat2x3.h b/include/cglm/call/mat2x3.h
index 90ff606..59c9ee3 100644
--- a/include/cglm/call/mat2x3.h
+++ b/include/cglm/call/mat2x3.h
@@ -27,11 +27,11 @@ glmc_mat2x3_make(const float * __restrict src, mat2x3 dest);
 
 CGLM_EXPORT
 void
-glmc_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest);
+glmc_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat3 dest);
 
 CGLM_EXPORT
 void
-glmc_mat2x3_mulv(mat2x3 m, vec3 v, vec2 dest);
+glmc_mat2x3_mulv(mat2x3 m, vec2 v, vec3 dest);
 
 CGLM_EXPORT
 void
diff --git a/include/cglm/mat2x3.h b/include/cglm/mat2x3.h
index 06fec14..3d5cedc 100644
--- a/include/cglm/mat2x3.h
+++ b/include/cglm/mat2x3.h
@@ -14,8 +14,8 @@
    CGLM_INLINE void glm_mat2x3_copy(mat2x3 mat, mat2x3 dest);
    CGLM_INLINE void glm_mat2x3_zero(mat2x3 mat);
    CGLM_INLINE void glm_mat2x3_make(const float * __restrict src, mat2x3 dest);
-   CGLM_INLINE void glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest);
-   CGLM_INLINE void glm_mat2x3_mulv(mat2x3 m, vec3 v, vec2 dest);
+   CGLM_INLINE void glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat3 dest);
+   CGLM_INLINE void glm_mat2x3_mulv(mat2x3 m, vec2 v, vec3 dest);
    CGLM_INLINE void glm_mat2x3_transpose(mat2x3 m, mat3x2 dest);
    CGLM_INLINE void glm_mat2x3_scale(mat2x3 m, float s);
  */
@@ -82,7 +82,7 @@ glm_mat2x3_make(const float * __restrict src, mat2x3 dest) {
  * @brief multiply m1 and m2 to dest
  *
  * @code
- * glm_mat2x3_mul(mat2x3, mat3x2, mat2);
+ * glm_mat2x3_mul(mat2x3, mat3x2, mat3);
  * @endcode
  *
  * @param[in]  m1   left matrix (mat2x3)
@@ -91,19 +91,25 @@ glm_mat2x3_make(const float * __restrict src, mat2x3 dest) {
  */
 CGLM_INLINE
 void
-glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest) {
-  float a00 = m1[0][0], a01 = m1[0][1], a02 = m1[0][2],
+glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat3 dest) {
+  float a00 = m1[0][0], a01 = m1[0][1], a02 = m1[0][2], 
         a10 = m1[1][0], a11 = m1[1][1], a12 = m1[1][2],
 
         b00 = m2[0][0], b01 = m2[0][1],
         b10 = m2[1][0], b11 = m2[1][1],
         b20 = m2[2][0], b21 = m2[2][1];
 
-  dest[0][0] = a00 * b00 + a01 * b10 + a02 * b20;
-  dest[0][1] = a00 * b01 + a01 * b11 + a02 * b21;
+  dest[0][0] = a00 * b00 + a10 * b01;
+  dest[0][1] = a01 * b00 + a11 * b01;
+  dest[0][2] = a02 * b00 + a12 * b01;
 
-  dest[1][0] = a10 * b00 + a11 * b10 + a12 * b20;
-  dest[1][1] = a10 * b01 + a11 * b11 + a12 * b21;
+  dest[1][0] = a00 * b10 + a10 * b11;
+  dest[1][1] = a01 * b10 + a11 * b11;
+  dest[1][2] = a02 * b10 + a12 * b11;
+
+  dest[2][0] = a00 * b20 + a10 * b21;
+  dest[2][1] = a01 * b20 + a11 * b21;
+  dest[2][2] = a02 * b20 + a12 * b21;
 }
 
 /*!
@@ -115,11 +121,14 @@ glm_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest) {
  */
 CGLM_INLINE
 void
-glm_mat2x3_mulv(mat2x3 m, vec3 v, vec2 dest) {
-  float v0 = v[0], v1 = v[1], v2 = v[2];
+glm_mat2x3_mulv(mat2x3 m, vec2 v, vec3 dest) {
+  float v0, v1;
 
-  dest[0] = m[0][0] * v0 + m[0][1] * v1 + m[0][2] * v2;
-  dest[1] = m[1][0] * v0 + m[1][1] * v1 + m[1][2] * v2;
+  v0 = v[0]; v1 = v[1];
+
+  dest[0] = m[0][0] * v0 + m[1][0] * v1;
+  dest[1] = m[0][1] * v0 + m[1][1] * v1;
+  dest[2] = m[0][2] * v0 + m[1][2] * v1;
 }
 
 /*!
diff --git a/include/cglm/struct/mat2x3.h b/include/cglm/struct/mat2x3.h
index 77084a7..3798893 100644
--- a/include/cglm/struct/mat2x3.h
+++ b/include/cglm/struct/mat2x3.h
@@ -14,7 +14,7 @@
    CGLM_INLINE mat2x3s glms_mat2x3_zero(void);
    CGLM_INLINE mat2x3s glms_mat2x3_make(const float * __restrict src);
    CGLM_INLINE mat2s   glms_mat2x3_mul(mat2x3s m1, mat3x2s m2);
-   CGLM_INLINE vec2s   glms_mat2x3_mulv(mat2x3s m, vec3s v);
+   CGLM_INLINE vec3s   glms_mat2x3_mulv(mat2x3s m, vec2s v);
    CGLM_INLINE mat3x2s glms_mat2x3_transpose(mat2x3s m);
    CGLM_INLINE mat2x3s glms_mat2x3_scale(mat2x3s m, float s);
  */
@@ -73,9 +73,9 @@ glms_mat2x3_(make)(const float * __restrict src) {
  * @returns destination matrix (mat2s)
  */
 CGLM_INLINE
-mat2s
+mat3s
 glms_mat2x3_(mul)(mat2x3s m1, mat3x2s m2) {
-  mat2s r;
+  mat3s r;
   glm_mat2x3_mul(m1.raw, m2.raw, r.raw);
   return r;
 }
@@ -85,12 +85,12 @@ glms_mat2x3_(mul)(mat2x3s m1, mat3x2s m2) {
  *
  * @param[in]  m    matrix (left)
  * @param[in]  v    vector (right, column vector)
- * @param[out] dest result vector
+ * @returns destination vector (vec3s)
  */
 CGLM_INLINE
-vec2s
-glms_mat2x3_(mulv)(mat2x3s m, vec3s v) {
-  vec2s r;
+vec3s
+glms_mat2x3_(mulv)(mat2x3s m, vec2s v) {
+  vec3s r;
   glm_mat2x3_mulv(m.raw, v.raw, r.raw);
   return r;
 }
diff --git a/src/mat2x3.c b/src/mat2x3.c
index dc5fd30..3397bf2 100644
--- a/src/mat2x3.c
+++ b/src/mat2x3.c
@@ -28,13 +28,13 @@ glmc_mat2x3_make(const float * __restrict src, mat2x3 dest) {
 
 CGLM_EXPORT
 void
-glmc_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat2 dest) {
+glmc_mat2x3_mul(mat2x3 m1, mat3x2 m2, mat3 dest) {
   glm_mat2x3_mul(m1, m2, dest);
 }
 
 CGLM_EXPORT
 void
-glmc_mat2x3_mulv(mat2x3 m, vec3 v, vec2 dest) {
+glmc_mat2x3_mulv(mat2x3 m, vec2 v, vec3 dest) {
   glm_mat2x3_mulv(m, v, dest);
 }
 
diff --git a/test/src/test_mat2x3.h b/test/src/test_mat2x3.h
index 7d615e4..8eb8144 100644
--- a/test/src/test_mat2x3.h
+++ b/test/src/test_mat2x3.h
@@ -83,42 +83,42 @@ TEST_IMPL(GLM_PREFIX, mat2x3_mul) {
   mat2x3 m1 = GLM_MAT2X3_ZERO_INIT;
   mat3x2 m2 = GLM_MAT3X2_ZERO_INIT;
 
-  mat2 m3 = GLM_MAT2_ZERO_INIT;
-  mat2 m4 = GLM_MAT2_ZERO_INIT;
+  mat3 m3 = GLM_MAT3_ZERO_INIT;
+  mat3 m4 = GLM_MAT3_ZERO_INIT;
 
-  int i, j, k;
+  int c, r, k;
 
   /* test random matrices */
   /* random matrices */
   test_rand_mat2x3(m1);
   test_rand_mat3x2(m2);
 
-  for (i = 0; i < 2; i++) {
-    for (j = 0; j < 2; j++) {
-      for (k = 0; k < 3; k++) {
-        m4[i][j] += m1[i][k] * m2[k][j];
+  for (r = 0; r < 3; r++) {
+    for (c = 0; c < 3; c++) {
+      for (k = 0; k < 2; k++) {
+        m4[c][r] += m1[k][r] * m2[c][k];
       }
     }
   }
 
   GLM(mat2x3_mul)(m1, m2, m3);
-  ASSERTIFY(test_assert_mat2_eq(m3, m4))
+  ASSERTIFY(test_assert_mat3_eq(m3, m4))
 
   TEST_SUCCESS
 }
 
 TEST_IMPL(GLM_PREFIX, mat2x3_mulv) {
   mat2x3 mat = A_MATRIX2X3;
-  vec3 v = {11.0f, 21.0f, 31.0f};
+  vec2 v = {11.0f, 21.0f};
 
   int  i;
-  vec2 dest;
+  vec3 dest;
   float res = 0.0;
 
   GLM(mat2x3_mulv)(mat, v, dest);
 
-  for (i = 0; i < 2; i++) {
-    res = mat[i][0] * v[0] + mat[i][1] * v[1] + mat[i][2] * v[2];
+  for (i = 0; i < 3; i++) {
+    res = mat[0][i] * v[0] + mat[1][i] * v[1];
     ASSERT(test_eq(dest[i], res))
   }