Most commutative operations encountered in practice are also associative. However, commutativity does not imply associativity. A counterexample is the function f ( x , y ) = x + y 2 , which is clearly commutative (interchanging x and y does not affect the result), but it is not associative (since, for example, f ( − − 4 , f ( 0 , + 4 ) ) = − − 1 but f ( f ( − − 4 , 0 ) , + 4 ) = + 1 ). More such examples may be found in commutative non-associative magmas. Furthermore, associativity does not imply commutativity either – for example multiplication of quaternions or of matrices is always associative but not always commutative.