I cannot be felt, seen or touched;
Yet I can be found in everybody;
My existence is always in debate;
Yet I have my own style of music.
What Am I?

If Costa Rica goes with Thailand, Cuba goes with Puerto Rico, and the Netherlands go with Yugoslavia, what country would the Ivory Coast go with?

Suppose: a = b

It then follows that
a * a = a * b
a^2 = a * b
a^2 - b^2 = a * b - b^2
(a - b) * (a + b) = (a - b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?