diff --git a/include/cglm/mat3.h b/include/cglm/mat3.h
index 7db616d..9d5f0d4 100644
--- a/include/cglm/mat3.h
+++ b/include/cglm/mat3.h
@@ -334,7 +334,7 @@ glm_mat3_det(mat3 mat) {
         d = mat[1][0], e = mat[1][1], f = mat[1][2],
         g = mat[2][0], h = mat[2][1], i = mat[2][2];
 
-  return a * (e * i - h * f) - d * (b * i - c * h) + g * (b * f - c * e);
+  return a * (e * i - h * f) - d * (b * i - h * c) + g * (b * f - e * c);
 }
 
 /*!
@@ -346,24 +346,22 @@ glm_mat3_det(mat3 mat) {
 CGLM_INLINE
 void
 glm_mat3_inv(mat3 mat, mat3 dest) {
-  float det;
   float a = mat[0][0], b = mat[0][1], c = mat[0][2],
         d = mat[1][0], e = mat[1][1], f = mat[1][2],
-        g = mat[2][0], h = mat[2][1], i = mat[2][2];
+        g = mat[2][0], h = mat[2][1], i = mat[2][2],
 
-  dest[0][0] =   e * i - f * h;
-  dest[0][1] = -(b * i - h * c);
-  dest[0][2] =   b * f - e * c;
-  dest[1][0] = -(d * i - g * f);
-  dest[1][1] =   a * i - c * g;
-  dest[1][2] = -(a * f - d * c);
-  dest[2][0] =   d * h - g * e;
-  dest[2][1] = -(a * h - g * b);
-  dest[2][2] =   a * e - b * d;
+        c1  = e * i - f * h, c2 = d * i - g * f, c3 = d * h - g * e,
+        idt = 1.0f / (a * c1 - b * c2 + c * c3), ndt = -idt;
 
-  det = 1.0f / (a * dest[0][0] + b * dest[1][0] + c * dest[2][0]);
-
-  glm_mat3_scale(dest, det);
+  dest[0][0] = idt * c1;
+  dest[0][1] = ndt * (b * i - h * c);
+  dest[0][2] = idt * (b * f - e * c);
+  dest[1][0] = ndt * c2;
+  dest[1][1] = idt * (a * i - g * c);
+  dest[1][2] = ndt * (a * f - d * c);
+  dest[2][0] = idt * c3;
+  dest[2][1] = ndt * (a * h - g * b);
+  dest[2][2] = idt * (a * e - d * b);
 }
 
 /*!