Is floating-point multiplication commutative? [duplicate]

Question

Floating point numbers are not exact due to its limited precision. My question is: is multiplication commutative in floating number computer calculation?

For example

double a = ..;
double b = ...;
double c = a * b;
double d = b * a;
if (c == d)
   cout << "Yes, great floating";

Answer 1

According to Wikipedia, yes, float multiplication is commutative.

While floating-point addition and multiplication are both commutative (a + b = b + a and a×b = b×a), they are not necessarily associative. That is, (a + b) + c is not necessarily equal to a + (b + c).