diff --git a/src/ssa/BinaryOp.go b/src/ssa/BinaryOp.go
index dc55a44..2ba4887 100644
--- a/src/ssa/BinaryOp.go
+++ b/src/ssa/BinaryOp.go
@@ -28,7 +28,11 @@ func (a *BinaryOp) Equals(v Value) bool {
 		return false
 	}
 
-	return a.Left.Equals(b.Left) && a.Right.Equals(b.Right)
+	if a.Left.Equals(b.Left) && a.Right.Equals(b.Right) {
+		return true
+	}
+
+	return a.IsCommutative() && a.Left.Equals(b.Right) && a.Right.Equals(b.Left)
 }
 
 // Inputs returns the left and right operands.
@@ -36,6 +40,16 @@ func (op *BinaryOp) Inputs() []Value {
 	return []Value{op.Left, op.Right}
 }
 
+// IsCommutative returns true if changing the order of the operands does not change the result.
+func (op *BinaryOp) IsCommutative() bool {
+	switch op.Op {
+	case token.Add, token.Mul, token.And, token.Or, token.Xor, token.LogicalAnd, token.LogicalOr, token.Equal, token.NotEqual:
+		return true
+	default:
+		return false
+	}
+}
+
 // IsPure returns true if both operands are constant.
 func (op *BinaryOp) IsPure() bool {
 	return op.Left.IsPure() && op.Right.IsPure()
diff --git a/tests/commutativity.q b/tests/commutativity.q
new file mode 100644
index 0000000..2b67baf
--- /dev/null
+++ b/tests/commutativity.q
@@ -0,0 +1,21 @@
+main() {
+	loop a := -10..10 {
+		loop b := -10..10 {
+			x := a + b
+			y := b + a
+			assert x == y
+			x = a * b
+			y = b * a
+			assert x == y
+			x = a & b
+			y = b & a
+			assert x == y
+			x = a | b
+			y = b | a
+			assert x == y
+			x = a ^ b
+			y = b ^ a
+			assert x == y
+		}
+	}
+}
\ No newline at end of file
diff --git a/tests/tests_test.go b/tests/tests_test.go
index f39fb31..74b3a31 100644
--- a/tests/tests_test.go
+++ b/tests/tests_test.go
@@ -77,6 +77,7 @@ var tests = []run{
 	{"loop-nested-xy", nil, "", "0,0\n0,1\n0,2\n1,0\n1,1\n1,2\n2,0\n2,1\n2,2\n", 0},
 	{"loop-nested-xyz", nil, "", "0,0,0\n0,0,1\n0,0,2\n0,1,0\n0,1,1\n0,1,2\n0,2,0\n0,2,1\n0,2,2\n1,0,0\n1,0,1\n1,0,2\n1,1,0\n1,1,1\n1,1,2\n1,2,0\n1,2,1\n1,2,2\n2,0,0\n2,0,1\n2,0,2\n2,1,0\n2,1,1\n2,1,2\n2,2,0\n2,2,1\n2,2,2\n", 0},
 	{"loop-nested-return", nil, "", "..........", 0},
+	{"commutativity", nil, "", "", 0},
 	{"factorial", nil, "", "", 0},
 	{"fibonacci", nil, "", "", 0},
 	{"memory", nil, "", "Hello\n", 0},