diff --git a/tests/xor.qc b/tests/xor.qc
index 81fb114..2006944 100644
--- a/tests/xor.qc
+++ b/tests/xor.qc
@@ -9,4 +9,16 @@ void main() {
     
     print(ftos(z), "\n");
     print(ftos(c), "\n");
+    
+    // commutative?
+    if (x ^ y == y ^ x)
+        print("commutative\n");
+    
+    // assocative?
+    if (x ^ (y ^ z) == (x ^ y) ^ z)
+        print("assocative\n");
+        
+    // elements are their own inverse?
+    if (x ^ 0 == x)
+        print("inverse\n");
 }
diff --git a/tests/xor.tmpl b/tests/xor.tmpl
index 681a982..0116161 100644
--- a/tests/xor.tmpl
+++ b/tests/xor.tmpl
@@ -5,3 +5,6 @@ C: -std=gmqcc
 E: $null
 M: 6
 M: 8
+M: commutative
+M: assocative
+M: inverse