diff --git a/include/cglm/quat.h b/include/cglm/quat.h
index d82a301..fa356d4 100644
--- a/include/cglm/quat.h
+++ b/include/cglm/quat.h
@@ -259,7 +259,7 @@ void
 glm_quat_inv(versor q, versor dest) {
   versor conj;
   glm_quat_conjugate(q, conj);
-  glm_vec_scale(conj, glm_vec4_norm2(q), dest);
+  glm_vec4_scale(conj, 1.0f / glm_vec4_norm2(q), dest);
 }
 
 /*!
diff --git a/test/src/test_quat.c b/test/src/test_quat.c
index fec8dae..74d12b5 100644
--- a/test/src/test_quat.c
+++ b/test/src/test_quat.c
@@ -26,6 +26,8 @@ test_quat(void **state) {
   /* 0. test identiy quat */
   glm_quat_identity(q4);
   assert_true(glm_quat_real(q4) == cosf(glm_rad(0.0f) * 0.5f));
+  glm_quat_mat4(q4, rot1);
+  test_assert_mat4_eq2(rot1, GLM_MAT4_IDENTITY, 0.000009);
 
   /* 1. test quat to mat and mat to quat */
   for (i = 0; i < 1000; i++) {
@@ -184,5 +186,14 @@ test_quat(void **state) {
   /* result must be identity */
   test_assert_mat4_eq2(rot1, GLM_MAT4_IDENTITY, 0.000009);
 
+  test_rand_quat(q3);
+
+  /* 12. inverse of quat, multiplication must be IDENTITY */
+  glm_quat_inv(q3, q4);
+  glm_quat_mul(q3, q4, q5);
+
+  glm_quat_identity(q3);
+  test_assert_quat_eq(q3, q5);
+
   /* TODO: add tests for slerp, lerp */
 }