diff --git a/matrix.cpp b/matrix.cpp
index 7c10857a..7d3bdf01 100644
--- a/matrix.cpp
+++ b/matrix.cpp
@@ -301,7 +301,7 @@ matrix<S,T>::look_at (util::point<3,T> eye,
         { 0, 0, 0, 1 }
     }};
 
-    return util::matrix4<T>::translation (-eye.template as<vector> ()) * rot;
+    return rot * util::matrix4<T>::translation (-eye.template as<vector> ());
 }
 
 
diff --git a/test/affine.cpp b/test/affine.cpp
index 66c3159a..4ecd4dfa 100644
--- a/test/affine.cpp
+++ b/test/affine.cpp
@@ -5,6 +5,40 @@
 #include "quaternion.hpp"
 
 
+///////////////////////////////////////////////////////////////////////////////
+void
+test_matrix_identities (util::TAP::logger &tap)
+{
+    static constexpr util::vector3f UP {0,1,0};
+
+    {
+        util::point3f p { 1, 2, 3 };
+
+        auto m = util::matrix4f::translation (0-p);
+        auto x = m * p.homog<4> ();
+        tap.expect_eq (x, util::point4f {0,0,0,1}, "trivial translation");
+    }
+
+    {
+        util::point3f eye { 1, 2, 3 };
+        util::point3f tgt { 0, 0, 0 };
+
+        auto m = util::matrix4f::look_at (eye, tgt, UP);
+        auto x = m * eye.homog<4> ();
+        tap.expect_eq (x, util::point4f {0,0,0,1}, "look_at eye translation");
+    }
+
+    {
+        util::point3f eye { 1, 2, 3 };
+        util::point3f tgt { 4, 5, 6 };
+
+        auto m = util::matrix4f::look_at (eye, tgt, UP);
+        auto x = m * eye.homog<4> ();
+        tap.expect_eq (x, util::point4f {0,0,0,1}, "look_at eye translation with target");
+    }
+}
+
+
 ///////////////////////////////////////////////////////////////////////////////
 void
 test_mq_axis (util::TAP::logger &tap)
@@ -66,6 +100,7 @@ main (int, char**)
 {
     util::TAP::logger tap;
 
+    test_matrix_identities (tap);
     test_mq_axis  (tap);
     test_mq_euler (tap);