Binary operation '*' defined as $a*b=a+b-ab$ on a set $A=R\setminus\left\{0,1\right\}$ where $R$ is Set of Reals
Is this binary operation closed under the above operation on above set $A$
I thought it is not closed since if $a=b=2$ then $$2*2=0$$ which is not in set $A$.
But my book answer is It is closed. What is my error?